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a. Suppose the profit per table increases by $100. Will this change the optimal production quantities? What can be said about the change in total profit? b. Suppose the profit per chair increases by $100. Will this change the optimal production quantities? What can be said about the change in total profit? c. Suppose the profit per table increases by $90 and the profit per bookcase decreases by $50. Will this change the optimal production quantities? What can be said about the change in total profit?

a. Suppose the profit per table increases by $100. Will this change the optimal production quantities? What can be said about the change in total profit? b. Suppose the profit per chair increases by $100. Will this change the optimal production quantities? What can be said about the change in total profit? c. Suppose the profit per table increases by $90 and the profit per bookcase decreases by $50. Will this change the optimal production quantities? What can be said about the change in total profit?

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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a. Suppose the profit per table increases by $100, Will this change the optimal production quantities? What can be said about the change in total profit? b. Suppose the profit per chair increases by $100. Will this change the optimal production quantities? What can be said about the change in total profit? c. Suppose the profit per table increases by $90 and the profit per bookcase decreases by $50. Will this change the optimal production quantities? What can be said about the change in total profit? d. Suppose a worker in the assembly department calls in sick, so eight fewer hours will be available tomorrow in the assembly department. How much would this affect total profit? Would it change the optimal production quantities? e. Explain why the shadow price for the wood constraint is zero.
Transcribed Image Text:a. Suppose the profit per table increases by $100, Will this change the optimal production quantities? What can be said about the change in total profit? b. Suppose the profit per chair increases by $100. Will this change the optimal production quantities? What can be said about the change in total profit? c. Suppose the profit per table increases by $90 and the profit per bookcase decreases by $50. Will this change the optimal production quantities? What can be said about the change in total profit? d. Suppose a worker in the assembly department calls in sick, so eight fewer hours will be available tomorrow in the assembly department. How much would this affect total profit? Would it change the optimal production quantities? e. Explain why the shadow price for the wood constraint is zero.
5.S1. Sensitivity Analysis at Stickley Furniture Stickley Furniture is a manufacturer of fine hand-crafted fur- niture. During the next production period (the eight-hour shift tomorrow), managcment is considcring producing dining room tables, dining room chairs, and/or bookcases. The time required for each item to go thmugh the two stages of production (assem- bly and finishing), the amount of wood required (fine cherry wood), and the corresponding unit profits are given in the fol- lowing table, along with the amount of each resource available in the upcoming production period. Tables Chairs Bookcases Available Assembly (minutes) 80 40 50 8,100 30 20 4,500 Finishing) (minutes) 30 Wood 80 10 50 9,000 (pounds) Unit profit $360 $125 $300 After formulating a linear programming model to determine the production levels that would maximize profit, the solved model and the corresponding sensitivity report are shown below.
Transcribed Image Text:5.S1. Sensitivity Analysis at Stickley Furniture Stickley Furniture is a manufacturer of fine hand-crafted fur- niture. During the next production period (the eight-hour shift tomorrow), managcment is considcring producing dining room tables, dining room chairs, and/or bookcases. The time required for each item to go thmugh the two stages of production (assem- bly and finishing), the amount of wood required (fine cherry wood), and the corresponding unit profits are given in the fol- lowing table, along with the amount of each resource available in the upcoming production period. Tables Chairs Bookcases Available Assembly (minutes) 80 40 50 8,100 30 20 4,500 Finishing) (minutes) 30 Wood 80 10 50 9,000 (pounds) Unit profit $360 $125 $300 After formulating a linear programming model to determine the production levels that would maximize profit, the solved model and the corresponding sensitivity report are shown below.
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