1. It is used to determine how the optimal solution is affected by changes, withinspecified ranges, in the2. What is sensitivity analysis?3. How is sensitivity analysis helpful?4. What do you need to use sensitivity analysis?5. In your own understanding, why don't we just re-solve the model if there is a change?6. How changes to any one of the objective function coefficients affect the optimalsolution?7. What is shadow price?

Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Answered: 1. It is used to determine how the…

Business

Management

1. It is used to determine how the optimal solution is affected by changes, within specified ranges, in the

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

See similar textbooks

Similar questions

If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…
Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0
b) Maximize Z = −40X1 −100X2s.t 10X1 + 5X2 ≤ 2502X1 + 5X2 ≤ 1002X1 + 3X2 ≤ 90X1, X2 ≥ 0Solve by simplex method, what are the solutions? Show that this problem hasmultiple solutions and find the solutions?
Based on Brams and Taylor (2000). Suppose that EliLilly and Pfizer are going to merge. Merger negotiations must settle the following issues: ■ What will the name of the merged corporation be?■ Will corporate headquarters be in Indianapolis(Lilly wants this) or New York (Pfizer wants this)?■ Which company’s chairperson will be chairperson of the merged corporation?■ Which company gets to choose the CEO?■ On the issue of layoffs, what percentage of each company’s view will prevail?Brams developed a remarkably simple method for the two adversaries to settle their differences. (This same method could be used to settle differences between other adversaries, such as a husband and wife in a divorce, Arab and Israel in Middle East, and so on.) Each adversary allocates 100 points between all of the issues. These allocations are listed in the file P04_84.xlsx. For example, Lilly believes headquarters is worth 30 points, whereas Pfizer thinks headquarters is worth only 15 points. Layoffs may be…
Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given below (round to two decimal places): Maximize 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0 a. The optimal value of A is 31.03 and the optimal value of B is 22.41. b. The maximized function yields a solution of 708.62. Chapter 7. For the problem you solved in Q1, obtain the Sensitivity Report, and answer the following questions. Remember to round to two digits and you can enter “infinity” for unlimited regions: The range for Variable A is from ????? to ????? The range for Variable B is from ????? to ????? The range for Constraint 1 is from ????? to ????? The range for Constraint 2 is from ????? to ????? The range for Constraint 3 is from ????? to ?????
Modern Machinery is trying to determine its product mix for next year. It produces two products , a mixture and a blender. Modern makes about $80 profit on each mixer and $60 on each blender. Modern's factory capacity is limited by labor, materials and machinery. Only 150,000 hours of labor are available next year, and each mixer uses 10 hours and each blender uses 5 hours. Only 300,000 pounds of steel are available next year, and each mixer uses 10 pounds and each blender uses 15 pounds. Only 190,000 machine hours are available next year, and each mixer uses 5 hours and each blender uses 4 hours. (a) How many mixers and blenders should Modern include in its business plan for next year? (b) How much profit will result?
Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3 Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700
3.Ruth Jones, the marketing manager for a department store chain is trying to decide on the optimal allocation of her advertising budget for the next quarter. Jones has the data that indicate that television commercials and newspaper advertisements have the following impact on sales revenue (R) R = 20,000T + 5000N + 20,000TN - 1O00T2 where T represents the number of commercials on T.V. and N the number of full-page newspaper advertisements. Each T.V. commercial costs $10,000 and each newspaper advertisement costs $5000. The advertising budget is limited to be $100,000. (a)Calculate the optimal amount of advertisement in each medium if the firm is interested in maximizing its sales revenue. Calculate the consequent value of sales revenue. (b)By how much should sales revenue increase if the advertising budget increases by a very small amount? Show and explain your calculations.
DynaTune is trying to determine how to allocate its $145,000advertising budget for a new product. Radio and television arethe two media outlets selected for advertising. Th e followingtable shows the costs of advertising in these two media and theestimated number of new customers reached by increasingamounts of advertising For example, each of the fi rst 10 ads the company places on theradio will cost $1000 and is expected to reach 900 new customers.Each of the next 10 will cost $900 and is expected to reach 700new customers. Assume the company will purchase no more than30 radio ads and no more than 15 television ads.(a) Formulate an LP to maximize the number of newcustomers reached.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution.(d) Suppose the number of new customers reached by 11–15television ads is 7500 and the number reached by 6–10ads is 5000. Resolve the problem. What is wrong with thissolution? Is Solver…
The Bargain Hut has 2400 cubic feet of storage space for refrigerators. Large refrigerators come in 60-cubic-foot packing crates and small refrigerators come in 40-cubic-foot crates. Large refrigeratorscan be sold for a $250 profit and the smaller ones can be sold for $150 profit. How many of each typeof refrigerator should be sold to maximize profit and what is the maximum profit if:a) If the manager wants to sell at least 50 refrigerators must be sold each month, how many large refrigerators and how many smaller refrigerators should he/she order each month to maximize profit?b) At least 40 refrigerators must be sold each month.
1. Explain your observations about the optimal solution returned by the Solver. 2. If the company has budget to increase the total capacity by 1,000 units, at which plant would you recommend them to expand? What would be total cost savings (i.e., potentially more reduction in the total costs) with this expansion? Refer to the sensitivity report and explain your answer. (Copy and paste the constraints section of the sensitivity report here.) 3. Suppose that the Atlanta plant had to reduce capacity by 1,000 units to repair and renovate. How much would this cause the total (optimized) transportation costs to increase? Refer to the sensitivity report and explain your answer. All i need is help with explaing these answers using the sensitivy reports and answer reports.