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Consider the following linear program: Min 8X + 12Y S.t. 1X +3Y 20 2X + 2Y 2 10 6X + 2Y 2 18 X, 1 20 a. Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. c. Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d. The sensitivity report for the linear program in part (a) provides the following objective coefficient range information Variable Y Objective Coefficient 8.000 12.000 Allowable Increase 4.000 12.000 Allowable Decrease 4.000 4.000 How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the problem?

Consider the following linear program: Min 8X + 12Y S.t. 1X +3Y 20 2X + 2Y 2 10 6X + 2Y 2 18 X, 1 20 a. Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. c. Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d. The sensitivity report for the linear program in part (a) provides the following objective coefficient range information Variable Y Objective Coefficient 8.000 12.000 Allowable Increase 4.000 12.000 Allowable Decrease 4.000 4.000 How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the problem?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Consider the following linear program: Min 8X + 12Y S.t. 1X + 3Y 29 2X + 2Y 2 10 6X + 2Y Z 18 X, 1 20 a. Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. c. Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d. The sensitivity report for the linear program in part (a) provides the following objective coefficient range information Variable Objective Coefficient 8.000 12.000 Allowable Increase 4.000 12.000 Allowable Decrease 4.000 4.000 How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the problem?
Transcribed Image Text:Consider the following linear program: Min 8X + 12Y S.t. 1X + 3Y 29 2X + 2Y 2 10 6X + 2Y Z 18 X, 1 20 a. Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. c. Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d. The sensitivity report for the linear program in part (a) provides the following objective coefficient range information Variable Objective Coefficient 8.000 12.000 Allowable Increase 4.000 12.000 Allowable Decrease 4.000 4.000 How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the problem?
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