Challenging Behaviour Essay

In this assignment my aim is to choose 3 ideas from chapters 1-3 of the textbook ‘Understanding Management’ (Cameron and Bridge, 2012), discuss why these ideas are important and finally describe how I have started to use them in everyday life this includes aspects of my work, leisure and home life. My 3 chosen ideas are SMART objectives, time management skills, and stress management. My first topic is the ‘SMART objectives’. ‘SMART’ is an acronym so each of the 5 letters have a specific meaning. Sometimes in the workplace it is easy to try and impose targets that seem out of reach. If targets are not clear it can sometimes be hard to measure whether a target has been met. In order to make it easier to manage the workforce’s performance clear and concise objectives must be set out. By using the SMART checklist employers can ensure that they have set relevant objectives. The letters ‘SMART’ stand for; ‘S’ – Specific – an employee/team member needs to be clear on his/her goal. ‘M’ – Measureable – means of measuring = means of control. ‘A’ – Achievable – the goal needs to be in reach otherwise a team will not try very hard. ‘R’ – Relevant – the objectives need to add up to the overall goal of which the manager is responsible. ‘T’ – Time defined. – In order to check progress time needs to be specified. (Cameron and Bridge, 2012) I have started to use this checklist in my work especially, as it gives a clear view on day to day goals. As a self-employed construction worker I need to be ‘Specific’ of what needs doing on a particular task. For example, before starting a job I need to specify the height, width of a wall with the client before work commences. Without these preferences the work that I carried out would be pointless as the client would most likely be disappointed. ‘Measure’ the overall progress of a task to be more efficient next time. For example, note down in a ‘works diary’ how long a particular job has taken to finish and use it as a bench mark for next time. Without a way of measuring progress a team would be insufficient. Liaise with my workforce and set ‘Achievable’ goals for the day’s work. Set targets that are in reach so as not to dishearten them. A disheartened workforce would shortfall the progression. ‘Relevance’ of the tools needed to carry out the work. At the end of each working day I like to plan ahead and make sure that I have all the relevant tools ready for the next day. Without these the work cannot be carried out therefore delaying our commitments with the client and generally causing stress and turmoil within the workforce. ‘Time defined’, the time I have to complete a job as I am often working to a tight schedule. For example some customers need certain work carried out/finished by a certain time due to their commitments. For example, recently a client wanted his garden feature completed in time before he was admitted to hospital for an operation. Time was of importance due to the clients commitments. My second idea is ‘Time management’ (Cameron and Bridge 2012). Time management is when you make a conscious decision on how to manage your time efficiently to ensure that you are able to complete each task you undergo with maximum effectiveness and efficiency. One way of improving your time management is to implement the ‘3 Es’ when you’re planning a task or an activity. The ‘3 Es’ have definitely been used in my own leisure/ hobby of taking on a course. The first ‘E’ (economy) has helped me in my essay work of firstly writing a plan. This has evidently helped in the time it will take in the actual essay writing because I have a guide. ‘Efficiently’ – I have kept my course work on a ‘PDF’ on my computer for me to access them more efficiently, this will save time when I need to access them quickly. I will use ‘Effectiveness’ to use my time wisely, for example not to start an essay 12a.m when my concentration is at its lowest. Stress Management (Cameron and Bridge, 2012) is my last idea. Stress can come from a number of different places. Stress is what occurs when someone is under a lot of pressure and their health is affected due to not being able to cope with certain pressures. Life is never simple therefore we will all feel a certain amount of stress at times this is normal however if there is a lot of stress for a prolonged amount of time this is when problems may arise. Prolonged stress can affect how well you are able to concentrate; it may impair your judgement and could also affect the standards of work. One of the first and simplest ways to manage your stress is to be aware of it. In the text ‘Understanding Management’ (Cameron and Bridges, 2012) there is a checklist that allows you to assess your own stress levels. This made me aware of certain things that may have been causing me undue stress in the workplace. After assessing my situation and considering what could be done to help relieve this I have started to do a few things differently when I am at work. A number of these things involve good planning. A day/workforce that has a plan will have no problems which will feedback no stress on the boss/manager (me). My last thoughts are on the importance of what I have learned from ‘Understanding Management’ (Cameron and Bridge, 2012). I feel that using the above strategies has evolved my way of thinking for the better in my work, leisure and home life therefore producing a more effective and professional approach to management. ********************************** Word count – 973 Reference list Cameron S. and Bridge K. (2012) Understanding Management, Milton Keynes, the Open University. TMA01 Task 2 On experiencing essay writing for the first time since secondary school, I felt the task a bit stressful and daunting. The most enjoyable and easiest task was reading chapters 1-3 ‘Understanding management’ in assignment booklet and note taking. I enjoyed it in school and enjoyed it now. The most difficult task was remembering to reference and where to reference. I often wondered if I was doing it enough or too much. This was down to no practice and lost touch with academic life. Another problem area was conclusion writing. 2. In the future I could research more on conclusion writing and reference writing to make this area a little easier. Also question my tutor. Word Count – 115

Sensitivity Analysis

Linear Programming Notes VII Sensitivity Analysis 1 Introduction When you use a mathematical model to describe reality you must make approximations. The world is more complicated than the kinds of optimization problems that we are able to solve. Linearity assumptions usually are signi? cant approximations. Another important approximation comes because you cannot be sure of the data that you put into the model. Your knowledge of the relevant technology may be imprecise, forcing you to approximate values in A, b, or c. Moreover, information may change.Sensitivity analysis is a systematic study of how sensitive (duh) solutions are to (small) changes in the data. The basic idea is to be able to give answers to questions of the form: 1. If the objective function changes, how does the solution change? 2. If resources available change, how does the solution change? 3. If a constraint is added to the problem, how does the solution change? One approach to these questions is to solve lots of l inear programming problems. For example, if you think that the price of your primary output will be between $100 and $120 per unit, you can solve twenty di? rent problems (one for each whole number between $100 and $120). 1 This method would work, but it is inelegant and (for large problems) would involve a large amount of computation time. (In fact, the computation time is cheap, and computing solutions to similar problems is a standard technique for studying sensitivity in practice. ) The approach that I will describe in these notes takes full advantage of the structure of LP programming problems and their solution. It turns out that you can often ? gure out what happens in â€Å"nearby† linear programming problems just by thinking and by examining the information provided by the simplex algorithm.In this section, I will describe the sensitivity analysis information provided in Excel computations. I will also try to give an intuition for the results. 2 Intuition and Overvie w Throughout these notes you should imagine that you must solve a linear programming problem, but then you want to see how the answer changes if the problem is changed. In every case, the results assume that only one thing about the problem changes. That is, in sensitivity analysis you evaluate what happens when only one parameter of the problem changes. 1 OK, there are really 21 problems, but who is counting? 1To ? x ideas, you may think about a particular LP, say the familiar example: max 2Ãâ€"1 subject to 3Ãâ€"1 x1 2x 1 + + + 4Ãâ€"2 x2 3Ãâ€"2 x2 + + + + 3x 3 x3 2x 3 3x 3 + + + x4 4x 4 3x 4 x4 x ? ? ? 12 7 10 0 We know that the solution to this problem is x0 = 42, x1 = 0; x2 = 10. 4; x3 = 0; x4 = . 4. 2. 1 Changing Objective Function Suppose that you solve an LP and then wish to solve another problem with the same constraints but a slightly di? erent objective function. (I will always make only one change in the problem at a time. So if I change the objective function, not onl y will I hold the constraints ? ed, but I will change only one coe cient in the objective function. ) When you change the objective function it turns out that there are two cases to consider. The ? rst case is the change in a non-basic variable (a variable that takes on the value zero in the solution). In the example, the relevant non-basic variables are x1 and x3 . What happens to your solution if the coe cient of a non-basic variable decreases? For example, suppose that the coe cient of x1 in the objective function above was reduced from 2 to 1 (so that the objective function is: max x1 + 4Ãâ€"2 + 3Ãâ€"3 + x4 ).What has happened is this: You have taken a variable that you didn’t want to use in the ? rst place (you set x1 = 0) and then made it less pro? table (lowered its coe cient in the objective function). You are still not going to use it. The solution does not change. Observation If you lower the objective function coe cient of a non-basic variable, then the solution does not change. What if you raise the coe cient? Intuitively, raising it just a little bit should not matter, but raising the coe cient a lot might induce you to change the value of x in a way that makes x1 > 0.So, for a non-basic variable, you should expect a solution to continue to be valid for a range of values for coe cients of nonbasic variables. The range should include all lower values for the coe cient and some higher values. If the coe cient increases enough (and putting the variable into the basis is feasible), then the solution changes. What happens to your solution if the coe cient of a basic variable (like x2 or x4 in the example) decreases? This situation di? ers from the previous one in that you are using the basis variable in the ? rst place. The change makes the variable contribute less to pro? . You should expect that a su ciently large reduction makes you want to change your solution (and lower the value the associated variable). For example, if the coe cient of x2 in the objective function in the example were 2 instead of 4 (so that the objective was max 2Ãâ€"1 +2Ãâ€"2 +3Ãâ€"3 + x4 ), 2 maybe you would want to set x2 = 0 instead of x2 = 10. 4. On the other hand, a small reduction in x2 ’s objective function coe cient would typically not cause you to change your solution. In contrast to the case of the non-basic variable, such a change will change the value of your objective function.You compute the value by plugging in x into the objective function, if x2 = 10. 4 and the coe cient of x2 goes down from 4 to 2, then the contribution of the x2 term to the value goes down from 41. 6 to 20. 8 (assuming that the solution remains the same). If the coe cient of a basic variable goes up, then your value goes up and you still want to use the variable, but if it goes up enough, you may want to adjust x so that it x2 is even possible. In many cases, this is possible by ? nding another basis (and therefore another solution).So, intuitively, t here should be a range of values of the coe cient of the objective function (a range that includes the original value) in which the solution of the problem does not change. Outside of this range, the solution will change (to lower the value of the basic variable for reductions and increase its value of increases in its objective function coe cient). The value of the problem always changes when you change the coe cient of a basic variable. 2. 2 Changing a Right-Hand Side Constant We discussed this topic when we talked about duality. I argued that dual prices capture the e? ct of a change in the amounts of available resources. When you changed the amount of resource in a non-binding constraint, then increases never changed your solution. Small decreases also did not change anything, but if you decreased the amount of resource enough to make the constraint binding, your solution could change. (Note the similarity between this analysis and the case of changing the coe cient of a non-bas ic variable in the objective function. Changes in the right-hand side of binding constraints always change the solution (the value of x must adjust to the new constraints).We saw earlier that the dual variable associated with the constraint measures how much the objective function will be in? uenced by the change. 2. 3 Adding a Constraint If you add a constraint to a problem, two things can happen. Your original solution satis? es the constraint or it doesn’t. If it does, then you are ? nished. If you had a solution before and the solution is still feasible for the new problem, then you must still have a solution. If the original solution does not satisfy the new constraint, then possibly the new problem is infeasible. If not, then there is another solution.The value must go down. (Adding a constraint makes the problem harder to satisfy, so you cannot possibly do better than before). If your original solution satis? es your new constraint, then you can do as well as before. I f not, then you will do worse. 2 2 There is a rare case in which originally your problem has multiple solutions, but only some of them satisfy the added constraint. In this case, which you need not worry about, 3 2. 4 Relationship to the Dual The objective function coe cients correspond to the right-hand side constants of resource constraints in the dual.The primal’s right-hand side constants correspond to objective function coe cients in the dual. Hence the exercise of changing the objective function’s coe cients is really the same as changing the resource constraints in the dual. It is extremely useful to become comfortable switching back and forth between primal and dual relationships. 3 Understanding Sensitivity Information Provided by Excel Excel permits you to create a sensitivity report with any solved LP. The report contains two tables, one associated with the variables and the other associated with the constraints.In reading these notes, keep the information i n the sensitivity tables associated with the ? rst simplex algorithm example nearby. 3. 1 Sensitivity Information on Changing (or Adjustable) Cells The top table in the sensitivity report refers to the variables in the problem. The ? rst column (Cell) tells you the location of the variable in your spreadsheet; the second column tells you its name (if you named the variable); the third column tells you the ? nal value; the fourth column is called the reduced cost; the ? fth column tells you the coe cient in the problem; the ? al two columns are labeled â€Å"allowable increase† and â€Å"allowable decrease. † Reduced cost, allowable increase, and allowable decrease are new terms. They need de? nitions. The allowable increases and decreases are easier. I will discuss them ? rst. The allowable increase is the amount by which you can increase the coe cient of the objective function without causing the optimal basis to change. The allowable decrease is the amount by which y ou can decrease the coe cient of the objective function without causing the optimal basis to change. Take the ? rst row of the table for the example. This row describes the variable x1 .The coe cient of x1 in the objective function is 2. The allowable increase is 9, the allowable decrease is â€Å"1. 00E+30,† which means 1030 , which really means 1. This means that provided that the coe cient of x1 in the objective function is less than 11 = 2 + 9 = original value + allowable increase, the basis does not change. Moreover, since x1 is a non-basic variable, when the basis stays the same, the value of the problem stays the same too. The information in this line con? rms the intuition provided earlier and adds something new. What is con? rmed is that if you lower the objective coe cient of a non-basic ariable, then your solution does not change. (This means that the allowable decrease will always be in? nite for a non-basic variable. ) The example also demonstrates your value wil l stay the same. 4 that increasing the coe cient of a non-basic variable may lead to a change in basis. In the example, if you increase the coe cient of x1 from 2 to anything greater than 9 (that is, if you add more than the allowable increase of 7 to the coe cient), then you change the solution. The sensitivity table does not tell you how the solution changes, but common sense suggests that x1 will take on a positive value.Notice that the line associated with the other non-basic variable of the example, x3 , is remarkably similar. The objective function coe cient is di? erent (3 rather than 2), but the allowable increase and decrease are the same as in the row for x1 . It is a coincidence that the allowable increases are the same. It is no coincidence that the allowable decrease is the same. We can conclude that the solution of the problem does not change as long as the coe cient of x3 in the objective function is less than or equal to 10. Consider now the basic variables. For x2 t he allowable increase is in? ite 9 while the allowable decrease is 2. 69 (it is 2 13 to be exact). This means that if the solution won’t change if you increase the coe cient of x2 , but it will change if you decrease the coe cient enough (that is, by more than 2. 7). The fact that your solution does not change no matter how much you increase x2 ’s coe cient means that there is no way to make x2 > 10. 4 and still satisfy the constraints of the problem. The fact that your solution does change when you increase x2 ’s coe cient by enough means that there is a feasible basis in which x2 takes on a value lower than 10. 4. You knew that. Examine the original basis for the problem. ) The range for x4 is di? erent. Line four of the sensitivity table says that the solution of the problem does not change provided that the coe cient of x4 in the objective function stays between 16 (allowable increase 15 plus objective function coe cient 1) and -4 (objective function coe cie nt minus allowable decrease). That is, if you make x4 su ciently more attractive, then your solution will change to permit you to use more x4 . If you make x4 su ciently less attractive the solution will also change. This time to use less x4 .Even when the solution of the problem does not change, when you change the coe cient of a basic variable the value of the problem will change. It will change in a predictable way. Speci? cally, you can use the table to tell you the solution of the LP when you take the original constraints and replace the original objective function by max 2Ãâ€"1 + 6Ãâ€"2 + 3Ãâ€"3 + x4 (that is, you change the coe cient of x2 from 4 to 6), then the solution to the problem remains the same. The value of the solution changes because now you multiply the 10. 4 units of x2 by 6 instead of 4. The objective function therefore goes up by 20. . The reduced cost of a variable is the smallest change in the objective function coe cient needed to arrive at a solution in which the variable takes on a positive value when you solve the problem. This is a mouthful. Fortunately, reduced costs are redundant information. The reduced cost is the negative of the allowable increase for non-basic variables (that is, if you change the coe cient of x1 by 7, then you arrive at a problem in which x1 takes on a positive 5 value in the solution). This is the same as saying that the allowable increase in the coe cient is 7.The reduced cost of a basic variable is always zero (because you need not change the objective function at all to make the variable positive). Neglecting rare cases in which a basis variable takes on the value 0 in a solution, you can ? gure out reduced costs from the other information in the table: If the ? nal value is positive, then the reduced cost is zero. If the ? nal value is zero, then the reduced cost is negative one times the allowable increase. Remarkably, the reduced cost of a variable is also the amount of slack in the dual constraint associated with the variable.With this interpretation, complementary slackness implies that if a variable that takes on a positive value in the solution, then its reduced cost is zero. 3. 2 Sensitivity Information on Constraints The second sensitivity table discusses the constraints. The cell column identi? es the location of the left-hand side of a constraint; the name column gives its name (if any); the ? nal value is the value of the left-hand side when you plug in the ? nal values for the variables; the shadow price is the dual variable associated with the constraint; the constraint R. H. ide is the right hand side of the constraint; allowable increase tells you by how much you can increase the right-hand side of the constraint without changing the basis; the allowable decrease tells you by how much you can decrease the right-hand side of the constraint without changing the basis. Complementary Slackness guarantees a relationship between the columns in the constraint table. The di? erence between the â€Å"Constraint Right-Hand Side† column and the â€Å"Final Value† column is the slack. (So, from the table, the slack for the three constraints is 0 (= 12 12), 37 (= 7 ( 30)), and 0 (= 10 10), respectively.We know from Complementary Slackness that if there is slack in the constraint then the associated dual variable is zero. Hence CS tells us that the second dual variable must be zero. Like the case of changes in the variables, you can ? gure out information on allowable changes from other information in the table. The allowable increase and decrease of non-binding variables can be computed knowing ? nal value and right-hand side constant. If a constraint is not binding, then adding more of the resource is not going to change your solution. Hence the allowable increase of a resource is in? ite for a non-binding constraint. (A nearly equivalent, and also true, statement is that the allowable increase of a resource is in? nite for a constraint w ith slack. ) In the example, this explains why the allowable increase of the second constraint is in? nite. One other quantity is also no surprise. The allowable decrease of a non-binding constraint is equal to the slack in the constraint. Hence the allowable decrease in the second constraint is 37. This means that if you decrease the right-hand side of the second constraint from its original value (7) to nything greater than 30 you do not change the optimal basis. In fact, the only part of the solution that changes when you do this is that the value of the slack variable for this constraint changes. In this paragraph, the point is only this: If you solve an LP and ? nd that a constraint is not binding, 6 then you can remove all of the unused (slack) portion of the resource associated with this constraint and not change the solution to the problem. The allowable increases and decreases for constraints that have no slack are more complicated. Consider the ? rst constraint.The informa tion in the table says that if the right-hand side of the ? rst constraint is between 10 (original value 12 minus allowable decrease 2) and in? nity, then the basis of the problem does not change. What these columns do not say is that the solution of the problem does change. Saying that the basis does not change means that the variables that were zero in the original solution continue to be zero in the new problem (with the right-hand side of the constraint changed). However, when the amount of available resource changes, necessarily the values of the other variables change. You can think about this in many ways. Go back to a standard example like the diet problem. If your diet provides exactly the right amount of Vitamin C, but then for some reason you learn that you need more Vitamin C. You will certainly change what you eat and (if you aren’t getting your Vitamin C through pills supplying pure Vitamin C) in order to do so you probably will need to change the composition of your diet – a little more of some foods and perhaps less of others. I am saying that (within the allowable range) you will not change the foods that you eat in positive amounts.That is, if you ate only spinach and oranges and bagels before, then you will only eat these things (but in di? erent quantities) after the change. Another thing that you can do is simply re-solve the LP with a di? erent right-hand side constant and compare the result. To ? nish the discussion, consider the third constraint in the example. The values for the allowable increase and allowable decrease guarantee that the basis that is optimal for the original problem (when the right-hand side of the third constraint is equal to 10) remains obtain provided that the right-hand side constant in this constraint is between -2. 333 and 12. Here is a way to think about this range. Suppose that your LP involves four production processes and uses three basic ingredients. Call the ingredients land, labor, and capi tal. The outputs vary use di? erent combinations of the ingredients. Maybe they are growing fruit (using lots of land and labor), cleaning bathrooms (using lots of labor), making cars (using lots of labor and and a bit of capital), and making computers (using lots of capital). For the initial speci? cation of available resources, you ? nd that your want to grow fruit and make cars.If you get an increase in the amount of capital, you may wish to shift into building computers instead of cars. If you experience a decrease in the amount of capital, you may wish to shift away from building cars and into cleaning bathrooms instead. As always when dealing with duality relationships, the the â€Å"Adjustable Cells† table and the â€Å"Constraints† table really provide the same information. Dual variables correspond to primal constraints. Primal variables correspond to dual constraints. Hence, the â€Å"Adjustable Cells† table tells you how sensitive primal variables and dual constraints are to changes in the primal objective function.The â€Å"Constraints† table tells you how sensitive dual variables and primal constraints are to changes in the dual objective function (right-hand side constants in the primal). 7 4 Example In this section I will present another formulation example and discuss the solution and sensitivity results. Imagine a furniture company that makes tables and chairs. A table requires 40 board feet of wood and a chair requires 30 board feet of wood. Wood costs $1 per board foot and 40,000 board feet of wood are available. It takes 2 hours of skilled labor to make an un? nished table or an un? ished chair. Three more hours of labor will turn an un? nished table into a ? nished table; two more hours of skilled labor will turn an un? nished chair into a ? nished chair. There are 6000 hours of skilled labor available. (Assume that you do not need to pay for this labor. ) The prices of output are given in the table below: Produ ct Un? nished Table Finished Table Un? nished Chair Finished Chair Price $70 $140 $60 $110 We want to formulate an LP that describes the production plans that the ? rm can use to maximize its pro? ts. The relevant variables are the number of ? nished and un? ished tables, I will call them TF and TU , and the number of ? nished and un? nished chairs, CF and CU . The revenue is (using the table): 70TU + 140TF + 60CU + 110CF , , while the cost is 40TU + 40TF + 30CU + 30CF (because lumber costs $1 per board foot). The constraints are: 1. 40TU + 40TF + 30CU + 30CF ? 40000. 2. 2TU + 5TF + 2CU + 4CF ? 6000. The ? rst constraint says that the amount of lumber used is no more than what is available. The second constraint states that the amount of labor used is no more than what is available. Excel ? nds the answer to the problem to be to construct only ? nished chairs (1333. 33 – I’m not sure what it means to make a sell 1 chair, but let’s assume 3 that this is possible) . The pro? t is $106,666. 67. Here are some sensitivity questions. 1. What would happen if the price of un? nished chairs went up? Currently they sell for $60. Because the allowable increase in the coe cient is $50, it would not be pro? table to produce them even if they sold for the same amount as ? nished chairs. If the price of un? nished chairs went down, then certainly you wouldn’t change your solution. 8 2. What would happen if the price of un? nished tables went up? Here something apparently absurd happens.The allowable increase is greater than 70. That is, even if you could sell un? nished tables for more than ? nished tables, you would not want to sell them. How could this be? The answer is that at current prices you don’t want to sell ? nished tables. Hence it is not enough to make un? nished tables more pro? table than ? nished tables, you must make them more pro? table than ? nished chairs. Doing so requires an even greater increase in the price. 3. What if the price of ? nished chairs fell to $100? This change would alter your production plan, since this would involve a $10 decrease in the price of ? ished chairs and the allowable decrease is only $5. In order to ? gure out what happens, you need to re-solve the problem. It turns out that the best thing to do is specialize in ? nished tables, producing 1000 and earning $100,000. Notice that if you continued with the old production plan your pro? t would be 70 ? 1333 1 = 93, 333 1 , so the change in production plan 3 3 was worth more than $6,000. 4. How would pro? t change if lumber supplies changed? The shadow price of the lumber constraint is $2. 67. The range of values for which the basis remains unchanged is 0 to 45,000.This means that if the lumber supply went up by 5000, then you would continue to specialize in ? nished chairs, and your pro? t would go up by $2. 67 ? 5000 = $10, 333. At this point you presumably run out of labor and want to reoptimize. If lumber supply decreased , then your pro? t would decrease, but you would still specialize in ? nished chairs. 5. How much would you be willing to pay an additional carpenter? Skilled labor is not worth anything to you. You are not using the labor than you have. Hence, you would pay nothing for additional workers. 6. Suppose that industrial regulations complicate the ? ishing process, so that it takes one extra hour per chair or table to turn an un? nished product into a ? nished one. How would this change your plans? You cannot read your answer o? the sensitivity table, but a bit of common sense tells you something. The change cannot make you better o?. On the other hand, to produce 1,333. 33 ? nished chairs you’ll need 1,333. 33 extra hours of labor. You do not have that available. So the change will change your pro? t. Using Excel, it turns out that it becomes optimal to specialize in ? nished tables, producing 1000 of them and earning $100,000. This problem di? ers from the original one because t he amount of labor to create a ? nished product increases by one unit. ) 7. The owner of the ? rm comes up with a design for a beautiful hand-crafted cabinet. Each cabinet requires 250 hours of labor (this is 6 weeks of full time work) and uses 50 board feet of lumber. Suppose that the company can sell a cabinet for $200, would it be worthwhile? You could solve this 9 problem by changing the problem and adding an additional variable and an additional constraint. Note that the coe cient of cabinets in the objective function is 150, which re? cts the sale price minus the cost of lumber. I did the computation. The ? nal value increased to 106,802. 7211. The solution involved reducing the output of un? nished chairs to 1319. 727891 and increasing the output of cabinets to 8. 163265306. (Again, please tolerate the fractions. ) You could not have guessed these ? gures in advance, but you could ? gure out that making cabinets was a good idea. The way to do this is to value the inputs to th e production of cabinets. Cabinets require labor, but labor has a shadow price of zero. They also require lumber. The shadow price of lumber is $2. 7, which means that each unit of lumber adds $2. 67 to pro? t. Hence 50 board feet of lumber would reduce pro? t by $133. 50. Since this is less than the price at which you can sell cabinets (minus the cost of lumber), you are better o? using your resources to build cabinets. (You can check that the increase in pro? t associated with making cabinets is $16. 50, the added pro? t per unit, times the number of cabinets that you actually produce. ) I attached a sheet where I did the same computation assuming that the price of cabinets was $150. In this case, the additional option does not lead to cabinet production. 10

Case study Example | Topics and Well Written Essays - 500 words - 24

Case Study Example This would mean that when the mathematical calculations are tallied in December they will be synthesized and far less than a genuine reflection of company’s exact numbers. But the â€Å"Christmas Bonus† would be present just as the manager wishes and is accustomed to. There is no question that this company’s yearly tradition will provide a better portfolio, but results in a far lower that acceptable ethical standard for all those who participate. The position that Terri is in is a difficult one. It is established that she is new to her position and eager to do the best possible job. Her manager asked her to change the numbers because the last person in her position had had no problem doing so. This directly reflects back to the questionable tactics of organizational socialization. She is presented with unethical tasks as if it common place and an everyday normality, and therefore acceptable. There is even a slight insinuation by the manager that is an expected part of her position. When faced with an ethical dilemma Holly Green, CEO and Managing Director of the Human Factor Consulting Firm, says, â€Å"You have to make decisions on whether you can live with it.†(qtd. in Balderrama, 2009) We all have a conscience, and it usually tells us when something just does not feel right. Often, people just don’t listen to it. She will have to make her decision and then stand by it. If she options not to do the unethical a ct requested there could be some unpleasant repercussions. This will, probably, not be the outright loss of employment, but she could face being passed over for promotions. In some worse case scenarios, the company may make her so miserable that she options to quit the company all on her own.(Zimmerman, 2010) So what does Terri do? Well that is what makes this so difficult. Doing the right thing should not be so hard. If

First Tennessee Bank (First Horizon National Corp) - Organizational Research Paper

First Tennessee Bank (First Horizon National Corp) - Organizational Behavior - Research Paper Example Organizational behavior is an integral aspect of various successful businesses. For a more precise understanding of the organizational behavior at FTB, it is important to identify certain norms and characteristics that determine the aspects of the regional bank. Some of these characteristics of organizational behavior include, firstly, attitudes and values of employees for example company culture, social responsibility and others. Secondly, motivation and performance, which encompass factors like, job security, bonuses, raises, and employee mentoring programs. Thirdly, managerial challenges for example global competition. The three factors play a significant role in shaping FTB’s organizational culture (Marquis& Huang, 2010). Employee work rate is governable by their perception or attitude towards the job they do. Such attitudes are achievable through values and ethics that dictate the manner in which organizational operations remain executed. Upholding workplace values and ethical practices ensures that there is no friction between the leadership of organizations and the junior employees. At FTB, the following are prevalent: Differentiated customer service considers the customer’s identities, in that, services are offered to customers automatically via a software system. An example is telematics, which is a component of information technology that deals with the transfer of digitized organizational information over long distances. FTB entered into a partnership with Ensenta Corporation, a software development organization. FTB is devoted to improving convenience for its customers and at the same time enhancing efficiency within the bank’s workforce. Therefore, Ensenta assists in achieving this goal by refining the remote deposit capture (RDC) service offered to customers. RDC is an information technology system that allows bank clients to scan checks from their diverse locations and send the images to FTB remotely through the

Healthcare post merger analysis Essay Example | Topics and Well Written Essays - 1500 words

Healthcare post merger analysis - Essay Example Consolidation in this industry is essential for its sustainable growth in the long run and to meet the emerging challenges in the industry in terms of huge investment and infrastructural facilities needed to cope up with the increased demand in the society for healthcare services. Evaluation of financial performance Study by Healy, Palepu & Ruback (1990) found that â€Å"The results indicate that merged firms have significant improvements in asset productivity relative to their industries after the merger, leading to higher post-merger operating cash flow returns.† The criteria for evaluating financial performance of the organizations post-merger are multifarious depending upon the type of organization and its objectives. However, in a typical company running on profit basis, return on investment post merger is an important criterion for evaluation of financial performance from the shareholders’ point of view. There are mergers also taking place between for profit and n ot for profit organizations. Financial and operating ratios as performance measures are adopted by the organizations for industry comparison as well as comparison with the historical performance. Of which, the following are the important ratios used for measuring performance in term of profitability. Return on assets : Net Income / Total Assets Return on equity : Net Income / Shareholders’ equity Return on capital employed : Earnings Before Interest and Tax (EBIT)/(Equity + Debt) Similarly, Earnings per Share (EPS), liquidity ratios, Cash flow ratios can be calculated for analysis and comparison. Budgetary analysis as a tool for evaluation will be effective as it reveals variances. This will enable the management to compare actual with the budgeted performance for exploring the reasons for variances and take corrective actions wherever necessary. Kumar (2012) stated â€Å"Between 1985 and 2007, 51 large companies in the industry consolidated into only 10 organizations†¦ they are effective methods of cutting costs.† Reduction in number of employees post merger, legal expenses, management cost and marketing costs are some of the areas where cost cutting is possible in the merged entity. Determinants of financial results post-merger It is important to determine whether or not the merger generated favourable financial results for the organization post merger. Section of Antitrust Law (2003, p.7-8) states â€Å"The size of the geographic will determine the number of competitors in the market, their market shares, and the likelihood of anticompetitive effects. Geographic definition issues have determined the outcome of the majority of hospital merger decisions.† Apart from improvements in operational performance due to synergies created in merger and environmental factors, it is important to note that the method of accounting, for example, purchase or acquisition method adopted for merger or type of financing (equity or debt) the merger has significant impact on the results of the merged organization from investment angle. Therefore, instead of profitability ratios, adopting pretax cash flows and increase or decrease thereof,

Job Satisfaction Essay Example | Topics and Well Written Essays - 1500 words

Job Satisfaction - Essay Example (1) Job satisfaction of the employees, and retaining them has become a growing concern in business organizations with the need to be more competitive, as a result of the growing globalization being witnessed. This stems from the belief that satisfied employees tend to be more productive, creative, and committed to the organization. There is evidence from the field of healthcare that job satisfaction among employees tend to make the healthcare organization more competitive in a market noted for its high rate of competitiveness. This competitiveness is through the improvement in quality and cost-effectiveness of satisfied employees. (2) Any discussion on job satisfaction needs to take into consideration the positive and negative factors of job satisfaction. According to Hezberg et al 1959, the positive factors known as motivators are achievement, recognition, the job responsibilities itself, and advancement opportunities. Negative factors known as hygiene factors include supervisors, fellow workers, company policy, workplace environment, and personal life. These findings of Hezberg et al were supported by studies conducted at the workplace, where workers were asked to present their perspectives of critical incidents that had occurred, but this remained the only manner in which the theory was supported. Wall et al in 1971, on the basis of confidentially collected data from workers, found that ego-defensive processes were responsible for the findings of Hezberg et al. These processes led to good events being the result of one’s own achievements, and bad events the due to the failings as a result of others. Thi s led to the general discarding of the Hezberg et al theory. However a subsequent study conducted in 1971, and as reported by Argyle, found relevance in the theory of Hezberg et al. This research on joy in workers found that while achievement was important, relationships

Unit 7&8 Essay Example | Topics and Well Written Essays - 1000 words

Unit 7 - Essay Example ingers and magicked things into existence makes the beauty and wonder of the Earth and the rest of our universe little more than a cheap conjuring trick† (Barnett, 2001, par. 14). He concluded that those who believe in the omnipotent power of a religious being as the creator of all things belittle the intelligence of the rest of mankind through the sheer disregard for the natural evolution of life. An atheist proclaims their total disbelief in any of the thousands of deities that millions of other people sincerely believe in. Atheism is total freedom from religious affiliations, values and beliefs. In this regard, atheists, like believers in other religions, respect the rights of others. Each person is entitled to his or her own beliefs. There is always a line between being a religious devotee and that of being a fanatic. The important thing to consider is respecting each other’s personal and religious orientations and beliefs. The evolution of domestic terrorism in the United States could be traced since the Civil War through the Vietnam War until contemporary times. A comprehensive report was written by the Federal Bureau of Investigation, one of the primary institutions in the country which is actively involved in studying terrorist activities. Their report entitled â€Å"Terrorism in the United States† was written to review and assess domestic terrorism in the United States within a thirty year period starting 1980s until 1999. The period under study revealed a drastic decrease in the frequency of domestic terrorist attacks as compared to levels recorded in the 1970s and 1980s. â€Å"Approximately 641 terrorist incidents occurred in the United States between 1971 and June 1975. Among these attacks were 166 bombings, 120 fire bombings, and 118 shootings.† (Terrorism in the United States, 1999, 29). From 1980 to 1999, of total terrorist attacks of 457, there were 321 bombings, 21 assassinations and 16 arson – with domestic terrorist attacks numbering 322

Spare the Rod, Spoil the Parenting by Leonard Pitts Essay

Spare the Rod, Spoil the Parenting by Leonard Pitts - Essay Example This research will begin with the biography of Leonard Pitts Jr. He was born in the United States and is a famous commentator, journalist, and an author. Leonard Pitts in his popular op-ed essay â€Å"spare the rod, spoil the parenting’’ makes use of a range of rhetorical or persuasive strategies to strengthen and support his opinions on the use of physical punishment to discipline children. The title of the story seems to be inspired from ‘He that spareth is a rod, hateth his son’ which is a biblical proverb. The proverb clearly portrays the importance of punishment. Leonard Pitt strives to persuade and educate parents regarding the importance that physical punishment has in the mental and intellectual development of children. Pitt tries to persuade his audiences to accept the fact that spanking and other forms of corporal punishments are necessary for forcing children to maintain discipline. Throughout the open format of the essay, Leonard Pitt uses a sa rcastic and blunt approach to not only spark reader’s interest but also to persuade them to accept his views. Therefore, the author tackles a sensitive topic in a casual yet authoritative manner which keeps his audiences intrigued till the very last line. The author’s strategy to use blunt diction and vocabulary to attract reader’s sympathy works phenomenally. In addition, Leonard Pitt argues and clearly points out the differences between corporal punishment ways and physical abuse, this argument forms the center of foci in his essay.... Pitt attempts to seek reader’s sympathy and understanding by stating that like most kids, his children are spoiled brats as well. Leonard makes use of his personal experience to convey to the readers that he is a parent who is capable of recognizing his children’s faults. In addition this strategy prevents the reader from thinking that the author is being judgmental towards others. The essay has an open format which makes the reader feel as if they are having a conversation with their best friend. Perhaps this is one of the most powerful rhetorical strategies used by the author throughout the essay. This allows the reader to take in and accept the information being conveyed by the author, without being intimated. Leonard maintains the strategy of having a conversation with his reader by asking questions such as ‘who is teaching whom?’ and ‘who is the in charge here?’This strategy not only ensures reader’s interest but also makes the read er realize that the author is not targeting a particular group of parents but in fact he is targeting the faults of all parents including him. He portrays the negative attributes of children by pointing out that they are ‘overindulged’ ‘spoiled’ and ‘materialistic brats’. Furthermore, the author blames his children to be bad and spoiled. This strategy forces the readers to sympathize with the author and realize that children need to be rewarded with a spank every time they misbehave. However, the author would never have been able to persuade the parents about the importance of corporal punishment if he had portrayed children as being good. Therefore, the author quotes ‘the screaming five year old’ and ‘misbehaving backside’ to reinforce his point that parents

Constitution Paper Essay Example for Free

Constitution Paper Essay The weaknesses in the Articles of Confederation were pointed out by the Constitution. The Articles of Confederation were tweaked in May 1786. This introduced a set of fresh regulations for the central government. Thedeclaration of Independence was approved by the Congress on July 4, 1776. The Constitution paid attention to the irregularities in the Declaration of Independence and replaced all direct mentions of slavery. The Great Compromise drew an end to the disagreements among the states and set congressional representation upon population on an equal basis. The Bill of Rights was introduced by James Madison to the first United States Congress on August 21 1789 and was used by the House of Representatives. John Dickinson proposed an outline to the Articles of Confederation in 1776. The first establishment of a formal government in the colonies was introduced in this. The Articles of Confederation was accepted by thirteen states on March 1 1781. The document of unification introduced a semblance of control to the central government. The Articles of Confederation helped address a feeble government system and pointed out a number of failures. Nonetheless The Articles of Confederation offered very little success as a government tool. The U.S. Constitution was put in writing in 1787. The new U.S. Constitution attempted to address the unsuccessful failures of the Articles of Confederation. For example, the Congress had no authority to charge taxes on the states. The system relied on donations from the states. The notion of federal taxation was opposed by the states. This caused an overpowering rise in currency because Congress did not have proper funding.Another defect of Congress was that it failed be in command of the foreign commerce. As a result, merchants and consumers had to pay high prices. Though Congress did possess the power to pass regulations and laws they were not allowed The thirteen American colonies of Great Britain revolted and declared independence for good reason. The actions of the British governm ent the king deprived Americans of numerous rights that were guaranteed to all other British citizens. In fact, many of these rights were guaranteed as early as 1215 since the American colonists were British citizens they had good reason to expect those rights to be recognized. They werent and in 1776 the American colonies declared independence and became the United States of America. When Americans wrote the Constitution and the Bill of Rights, they made sure to fix the problems.  These are some of the ways they fix the problems The king exercised absolute power. The power of British kings had been limited since 1215 almost 400 years before the first American colony was settled. The US Constitution divides power among three branches of government, and there are checks and balances to make sure that no single branch gets too powerful. Colonials were taxed without their consent. British citizens were represented in Parliament American colonists were not represented in Parliament, even though they were British citizens The US Constitution gives Congress the power to tax US citizens, and US citizens are represented in Congress by representatives they elect. July 16, 1987 began with a light breeze a cloudless sky and a spirit of celebration. On that day two hundred senators and representatives boarded a special train for a journey to Philadelphia to celebrate a sing ular congressional anniversary. Exactly two hundred years earlier the framers of the U.S. Constitution, meeting at Independence Hall, had reached a supremely important agreement. Their so called Great Compromise Connecticut Compromise in honor of its architects Connecticut delegates Roger Sherman and Oliver Ellsworth provided a dual system of congressional representation. In the House of Representatives each state would be assigned a number of seats in proportion to its population. In the Senate all states would have the same number of seats. Today we take this arrangement for granted in the wilting hot summer of 1787 it was a new idea. In the weeks before July 16 1787 the framers had made several important decisions about the Senates structure. They turned aside a proposal to have the House of Representatives elect senators from lists submitted by the individual state legislatures and agreed that those legislatures should elect their own senators. By July 16 the convention had already set the minimum age for senators at thirty and the term length at six years as opposed to twenty-five for House members with two year terms. James Madison explained that these distinctions based on the nature of the senatorial trust, which requires greater extent of information and stability of character would allow the Senate to proceed with more coolness with more system and with more wisdom than the popular electedbranch The issue of representation however threatened to destroy the seven week old convention. Delegates from the large states believed that because their states contributed proportionally more to the nations financial and defensive  resources they should enjoy proportionally greater representation in the Senate as well as in the House. Small-state delegates demanded, with comparable intensity, that all states be equally represented in both houses. When Sherman proposed the compromise, Benjamin Franklin agreed that each state should have an equal vote in the Senate in all mattersexcept those involving money. Over the Fourth of July holiday delegates worked out a compromise plan that sidetracked Franklins proposal. On July 16 the convention adopted the Great Compromise by a heart stopping margin of one vote. As the 1987 celebrants duly noted without that vote there would likely have been no Constitution. I think the bill of rights would be the perfect discussion what is the bill of rights The original Constitution as proposed in 1787 in Philadelphia and as ratified by the sta tes, contained very few individual rights guarantees as the framers were primarily focused on establishing the machinery for an effective federal government. A proposal by delegate Charles Pinckney to include several rights guarantees including liberty of the press and a ban on quartering soldiers in private homes was submitted to the Committee on Detail on August 20 1787 but the Committee did not adopt any of Pinckney recommendations. The matter came up before the Convention on September 12 1787 and following a brief debate proposals to include a Bill or Rights in the Constitution were rejected. As adopted, the Constitution included only a few specific rights guarantees protection against states impairing the obligation of contracts provisions that prohibit both the federal and state governments from enforcingex post facto lawslaws that allow punishment for an action that was not criminal at the time it was undertaken and provisions barringbills of attainderlegislative determinations of guilt and punishment Art. I Sections 9 and 10. The framers and notably James Madison its principal architect believed that the Constitution protected lib erty primarily through its division of powers that made it difficult for an oppressive majorities to form and capture power to be used against minorities. Delegates also probably feared that a debate over liberty guarantees might prolong or even threaten the fiercely-debated compromises that had been made over the long hot summer of 1787. In the ratification debate Ant Federalists opposed to the Constitution complained that the new system threatened liberties and suggested that if the delegates had truly cared about protecting individual rights they would have included  provisions that accomplished that. With ratification in serious doubt Federalists announced a willingness to take up the matter of series of amendments to be called the Bill of Rights soon after ratification and the First Congress comes into session. The concession wasundoubtedlynecessary to secure the Constitutions hard fought ratification. Thomas Jefferson, who did not attend the Constitutional Convention,in a December 1787 letter to Madisoncalled the omission of a Bill of Rights a major mistake A bill of rights is what the people are entitled to against every government on earth. James Madison was skeptical of the value of a listing of rights, calling it a parchment barrier. Madisons preference at the Convention to safeguard liberties was by giving Congress an unlimited veto over state laws and creating a joint executive judicial council of revision that could veto federal laws. Despite his skepticism, by the fall of 1788 Madison believed that a declaration of rights should be added to the Constitution. Its value, in Madisons view, was in part educational, in part as a vehicle that might be used to rally people against a future oppressive government and finally in an argumentborrowed from Thomas Jefferson Madison argued that a declaration of rights would help install the judiciary as guardian ofindividual rights against the other branches.

Hero and Mrs. Fisher Essay Example for Free

Hero and Mrs. Fisher Essay Heroism is a role model and someone who helps others with out personal gain or need, and they show support. Tangerine by Edward Bloor contains characters that are heroes and non-heroes. Paul Fisher is a hero while his brother, Erik, is not and Mrs. Fisher also has traits of heroism. Paul Fisher is a hero because he puts others before himself despite personal danger and because he does the right thing without need for personal gain. Paul helps people during the sinkhole incident at lake Windser Middle School. He saves other classmates and teachers from the portable classrooms, ensuring their safety (80). This shows Paul is brave and willing to protect his classmates in a horrible accident. Besides the sinkhole, Paul aids to the Cruz family during the freeze. He brings wood to Luis and chopped ice off trees, doing whatever they could to get a majority of them saved (214, 215). Paul helps the Cruz family without being asked to. He lies to his mom so she would let him stay and help (210, 213). Paul was committed to save the tangerine trees of Tangerine. Since Paul is friendly to people, he always has his friends backs and he understands them. Paul defended fire fighter Wayne when Mr. Fisher strongly complained about his unprofessional appearance (22). Paul figured that Wayne didn’t deserve a complaint when he knew what he was talking about. Paul also gave Joey Costello advice to move schools and become a War Eagle (121). Joey took the advice and moved schools, and he joined their soccer team. Paul didn’t want Joey to be unhappy with his new school hours, so he suggested Tangerine High. Paul looks out for his friends and is very encouraging. Besides Paul Fisher being a hero, his mom, Mrs. Fisher, also shows examples of heroism. Mrs. Fisher is a helpful citizen and cares about everyone’s safety. She hosts a parent gathering to discuss their sons’ football practice times (54- 55). Mrs. Fisher tries changing practice times so no other player will be struck by lightning, like Mike Costello. Additionally, Mrs. Fisher shows her safety concerns to Paul’s school about his eyesight, so he could have extra help (24). She wanted to do what was best for Paul but she wanted him to have to opportunity to play soccer. When Paul moved schools, she realized the best thing would be is not to inform them about him eye conditions, that way he would be able to play soccer. Not only is Mrs. Fisher concerned about safety; she is also supportive to her family and friends. Mrs. Fisher supports Erik by attending his football games (124, 125). She encourages and cheers for Erik while he kicks. She is proud of his hard work and accomplishments. Another way Mrs. Fisher is supportive is when she shows sympathy to the Costello family. Mrs. Fisher attends Mike Costello’s funeral and explains how sorry she was and gives love and supportive gestures to acknowledge her sympathy. While Paul Fisher and Mrs. Fisher both are explained through heroism, Erik Fisher is a non-hero. Erik is very selfish and only cares about him and has success as an individual. Erik is an amazing kicker; he always bragged about his skills and was convinced that he will be a star one-day. All he cares about is football and his future of football (20, 21). Erik thought he was better than everyone else. He was happy when Mike was killed because he knew he would benefit from it (51). Furthermore, Erik is also a non-hero because he is a bully. Erik makes fun of Joey because he tried to take off his brother’s shoes when he was dead. Erik didn’t know the real reason why he did that, he just noticed it and judged him poorly (110). Erik doesn’t care about how anyone feels or how he makes him or her feel; he amuses himself with their emotional pain. Erik also makes fun of Paul about his glasses. Erik called Paul â€Å"Eclipse Boy† and made up stories about how Paul’s eyesight failed (2, 54). Heroism is someone that puts others before themselves and is a role model. Paul and Mrs. Fisher are both heroes while Erik is not. The author wrote this story because he is a middle school teacher and wanted to share a story that exampled students in ways they are heroes. There are more heroes than there are non-heroes. Edward Bloor wrote this book for middle age kids so he tried to focus on the positive sides of people. There are heroes all around you but everyone has non-hero moments, you should learn from your mistakes.