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an introduction to management science

Questions and Answers of An Introduction to Management Science

=e. Find an optimal solution under each scenario after making the necessary adjustments to the linear programming model formulated in partb. In each case, what is the prediction regarding the
=f. For the optimal solution obtained under each of the six scenarios (including the good weather scenario considered in parts a–d), calculate what the family’s monetary worth would be at the
=g. Modify the linear programming model formulated in part b to fit this new approach.
=h. Repeat part c for this modified model.
=i. Use a shadow price obtained in part h to analyze whether it would be worthwhile for the family to obtain a bank loan with a 10 percent interest rate to purchase more livestock now beyond what can
=j. For each of the three crops, use the sensitivity report obtained in part h to identify how much latitude for error is available in estimating the net value per acre planted for that crop without
=k. Think about specific situations outside of farm management that fit this description. Describe one.
=a. If you have not already done so for part a of Case 3-5, formulate and solve a linear programming model for this problem on a spreadsheet.
=b. Use the Solver to generate the sensitivity report.One concern of the school board is the ongoing road construction in area 6. These construction projects have been delaying traffic considerably
=c. Use the sensitivity report to check how much the busing cost from area 6 to school 1 can increase (assuming no change in the costs for the other schools) before the current optimal solution would
=d. Repeat part c for school 2 (assuming no change in the costs for the other schools).
=e. Now assume that the busing cost from area 6 would increase by the same percentage for all the schools. Use the sensitivity report to determine how large this percentage can be before the current
=f. For each school, use the corresponding shadow price from the sensitivity report to determine whether it would be worthwhile to add any portable classrooms.
=g. For each school where it is worthwhile to add any portable classrooms, use the sensitivity report to determine how many could be added before the shadow price would no longer be valid(assuming
=h. If it would be worthwhile to add portable classrooms to more than one school, use the sensitivity report to determine the combinations of the number to add for which the shadow prices definitely
=i. If part h was applicable, modify the best combination of portable classrooms found there by adding one more to the school with the most favorable shadow price. Use the Solver to find the
=5.1.* One of the products of the G. A. Tanner Company is a special kind of toy that provides an estimated unit profit of $3.Because of a large demand for this toy, management would like to increase
=E*a. Formulate and solve a spreadsheet model for this Unit profit $2 $5 problem.
=E*b. Since the stated unit profits for the two activities are only estimates, management wants to know how much each of these estimates can be off before the optimal solution would change. Begin
=E*c. Repeat part b for the second activity (producing subassemblies) by generating a table as the unit profit for this activity increases in 50¢ increments from $3.50 to $1.50 (with the unit profit
=E*d. Use the Solver Table to systematically generate all the data requested in parts b andc, except use 25¢ increments instead of 50¢ increments. Use these data to refine your conclusions in parts
=E*e. Use Excel’s sensitivity report to find the allowable range for the unit profit of each activity.
=E*f. Use a two-way Solver Table to systematically generate the total profit as the unit profits of the two activities are changed simultaneously as described in parts b and c.
=g. Use the information provided by Excel’s sensitivity report to describe how far the unit profits of the two activities can change simultaneously before the optimal solution might change.
=5.2. Consider a resource-allocation problem having the following data:Resource Usage per Unit of Each Activity Amount of Resource Resource 1 2 Available 1 1 2 10 2 1 3 12
=E*a. Formulate and solve a spreadsheet model for this Unit profit $2 $5 While doing what-if analysis, you learn that the estimates of the unit profits are accurate only to within 50 percent. In
=E*a. Formulate a spreadsheet model for this problem based on the original estimates of the unit profits.Then use the Solver to find an optimal solution and to generate the sensitivity report.
=E*b. Use the spreadsheet and Solver to check whether this optimal solution remains optimal if the unit profit for activity 1 changes from $2 to $1. From$2 to $3.
=E*c. Also check whether the optimal solution remains optimal if the unit profit for activity 1 still is $2 but the unit profit for activity 2 changes from $5 to$2.50. From $5 to $7.50.
=E*d. Use the Solver Table to systematically generate the optimal solution and total profit as the unit profit of activity 1 increases in 20¢ increments from $1 to $3(without changing the unit
=e. Use the Graphical Linear Programming and Sensitivity Analysis module in your Interactive Management Science Modules to estimate the allowable range for the unit profit of each activity.
=E*f. Use the sensitivity report to find the allowable range for the unit profit of each activity. Then use these ranges to check your results in parts b–e.
=E* g. Use a two-way Solver Table to systematically generate the optimal solution as the unit profits of the two activities are changed simultaneously as described in part d.
=h. Use the Graphical Linear Programming and Sensitivity Analysis module to interpret the results in part g graphically.
=E*5.3. Consider the Big M Co. problem presented in Section 3.5, including the spreadsheet in Figure 3.10 showing its formulation and optimal solution.There is some uncertainty about what the unit
=a. Which of the unit shipping costs given in Table 3.9 has the smallest margin for error without invalidating the optimal solution given in Figure 3.10? Where should the greatest effort be placed
=b. What is the allowable range for each of the unit shipping costs?
=c. How should the allowable range be interpreted to management?
=d. If the estimates change for more than one of the unit shipping costs, how can you use the sensitivity report to determine whether the optimal solution might change?
=E*5.4.* Consider the Union Airways problem presented in Section 3.3, including the spreadsheet in Figure 3.5 showing its formulation and optimal solution.Management is about to begin negotiations
=f. Use the Solver to generate the sensitivity report for this problem. Suppose that the above changes are being considered later without having the spreadsheet model immediately available on a
=g. For each of the five shifts in turn, use the Solver Table to systematically generate the optimal solution and total cost when the only change is that the daily cost per agent on that shift
=E*5.5. Consider the Think-Big Development Co. problem presented in Section 3.2, including the spreadsheet in Figure 3.3 showing its formulation and optimal solution. In parts a–g, use the
=a. The net present value of project 1 (a high-rise office building) increases by $200,000.
=b. The net present value of project 2 (a hotel) increases by $200,000.
=c. The net present value of project 1 decreases by$5 million.
=d. The net present value of project 3 (a shopping center) decreases by $200,000.
=e. All three changes in partsb, c, and d occur simultaneously.
=f. The net present values of projects 1, 2, and 3 change to$46 million, $69 million, and $49 million, respectively
=g. The net present values of projects 1, 2, and 3 change to $54 million, $84 million, and $60 million, respectively.
=h. Use the Solver to generate the sensitivity report for this problem. For each of the preceding parts, suppose that the change occurs later without having the spreadsheet model immediately
=i. For each of the three projects in turn, use the Solver Table to systematically generate the optimal solution and the total net present value when the only change is that the net present value of
=5.6. Read the referenced article that fully describes the management science study summarized in the application vignette presented in Section 5.4. Briefly describe how what-if analysis was applied
=5.7. University Ceramics manufactures plates, mugs, and steins that include the campus name and logo for sale in campus bookstores. The time required for each item to go through the two stages of
=a. Suppose the profit per plate decreases from $3.10 to$2.80. Will this change the optimal production quantities? What can be said about the change in total profit?
=b. Suppose the profit per stein increases by $0.30 and the profit per plate decreases by $0.25. Will this change the optimal production quantities? What can be said about the change in total profit?
=c. Suppose a worker in the molding department calls in sick. Now eight fewer hours are available that day in the molding department. How much would this affect total profit? Would it change the
=d. Suppose one of the workers in the molding department is also trained to do finishing. Would it be a good idea to have this worker shift some of her time from the molding department to the
=e. The allowable decrease for the mugs’ objective coefficient and for the available clay constraint are both missing from the sensitivity report. What numbers should be there? Explain how you
=5.8. Ken and Larry, Inc., supplies its ice cream parlors with three flavors of ice cream: chocolate, vanilla, and banana. Due to extremely hot weather and a high demand for its products, the company
=a. What is the optimal solution and total profit?
=b. Suppose the profit per gallon of banana changes to$1.00. Will the optimal solution change and what can be said about the effect on total profit?
=c. Suppose the profit per gallon of banana changes to 92¢. Will the optimal solution change and what can be said about the effect on total profit?
=d. Suppose the company discovers that three gallons of cream have gone sour and so must be thrown out.Will the optimal solution change and what can be said about the effect on total profit?
=e. Suppose the company has the opportunity to buy an additional 15 pounds of sugar at a total cost of $15.Should it do so? Explain.
=f. Fill in all the sensitivity report information for the milk constraint, given just the optimal solution for the problem. Explain how you were able to deduce each number.
=5.9. Colonial Furniture produces hand-crafted colonial style furniture. Plans are now being made for the production of rocking chairs, dining room tables, and/or armoires over the next week.These
=a. Suppose the profit per armoire decreases by$50. Will this change the optimal production quantities? What can be said about the change in total profit?
=b. Suppose the profit per table decreases by $60 and the profit per armoire increases by $90. Will this change the optimal production quantities? What can be said about the change in total profit?
=c. Suppose a part-time worker in the assembly department calls in sick, so that now four fewer hours are available that day in the assembly department. How much would this affect total profit?
=d. Suppose one of the workers in the assembly department is also trained to do finishing. Would it be a good idea to have this worker shift some of his time from the assembly department to the
=e. The shadow price and allowable range for the wood constraint are missing from the sensitivity report.What numbers should be there? Explain how you were able to deduce each number.
=5.10. David, LaDeana, and Lydia are the sole partners and workers in a company that produces fine clocks. David and LaDeana are each available to work a maximum of 40 hours per week at the company,
=a. Formulate a linear programming model in algebraic form for this problem.
=b. Use the Graphical Linear Programming and Sensitivity Analysis module in your Interactive Management Science Modules to solve the model. Then use this module to check if the optimal solution
=E*c. Formulate and solve the original version of this model on a spreadsheet.
=E*d. Use the Excel Solver to check the effect of the changes specified in part b.
=E*e. Use the Solver Table to systematically generate the optimal solution and total profit as the unit profit for grandfather clocks is increased in $20 increments from $150 to $450 (with no change
=E*f. Use a two-way Solver Table to systematically generate the optimal solution (similar to Figure 5.13) as the unit profits for the two types of clocks are changed simultaneously as specified in
=E* g. For each of the three partners in turn, use the Excel Solver to determine the effect on the optimal solution and the total profit if that partner alone were to increase his or her maximum
=E* h. Use the Solver Table to systematically generate the optimal solution and the total profit when the only change is that David’s maximum number of hours available to work per week changes to
=E* i. Generate the Excel sensitivity report and use it to determine the allowable range for the unit profit for each type of clock and the allowable range for the maximum number of hours each
=j. To increase the total profit, the three partners have agreed that one of them will slightly increase the maximum number of hours available to work per week. The choice of which one will be based
=k. Explain why one of the shadow prices is equal to zero.
=l. Can the shadow prices in the sensitivity report be validly used to determine the effect if Lydia were to change her maximum number of hours available to work per week from 20 to 25? If so, what
=E*5.11.* Reconsider Problem 5.1. After further negotiations with each vendor, management of the G.A. Tanner Company has learned that either of them would be willing to consider increasing their
=b. Without considering the premium, use the spreadsheet and Solver to determine the shadow price for the subassembly A constraint by solving the model again after increasing the maximum supply by
=c. Repeat part b for the subassembly B constraint.d. Estimate how much the maximum supply of subassemblies of type A could be increased before the
=shadow price (and the corresponding premium)found in part b would no longer be valid by using the Solver Table to generate the optimal solution and total profit (excluding the premium) as the
=E*5.12. Reconsider the model given in Problem 5.2. While doing what-if analysis, you learn that the estimates of the righthand sides of the two functional constraints are accurate only to within 50
=5.13. Consider a resource-allocation problem having the following data:Resource Usage per Unit of Each Activity Amount of Resource Resource 1 2 Available 1 1 3 8 2 1 1 4 Unit profit $1 $2 The
=E*c. Use the spreadsheet model and the Solver instead to do parts a and b.
=E*d. For each resource in turn, use the Solver Table to systematically generate the optimal solution and the total profit when the only change is that the amount of that resource available
=E*e. Use the Solver’s sensitivity report to obtain the shadow prices. Also use this report to find the range for the amount of each resource available over which the corresponding shadow price
=5.14. Follow the instructions of Problem 5.13 for a resourceallocation problem that again has the objective of maximizing total profit and that has the following data:Resource Usage per Unit of
=E*5.15.* Consider the Super Grain Corp. case study as presented in Section 3.1, including the spreadsheet in Figure 3.1 showing its formulation and optimal solution. Use the Excel Solver to
=a. How much could the total expected number of exposures be increased for each additional $1,000 added to the advertising budget?
=b. Your answer in part a would remain valid for how large of an increase in the advertising budget?c. How much could the total expected number of
=exposures be increased for each additional $1,000 added to the planning budget?
=d. Your answer in part c would remain valid for how large of an increase in the planning budget?

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