During the next production period, The Diego Garcia Furniture Company is considering producing dining room chairs, dining room tables and/or bookcases. Each item must go through the two stages of production (assembly and finishing), and requires a certain amount of wood (fine cherry wood). They have formulated a linear program to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below. A B D E F G 1 Chairs Tables Bookcases 2 Unit Profit $40 $220 $280 3 4 Resources Required per Unit Total Used Available 5 Assembly (minutes) Finishing (minutes) Wood (pounds) 20 30 45 3600 く= 3600 10 20 20 2000 <= 2000 7 10 30 45 3600 く= 3800 8 9 Chairs Tables Bookcases Total Profit 10 Prodution 60 40 $24,400 Variable Cells Objective Coefficient Final Reduced Allowable Allowable Cell Name Value Cost Increase Decrease $B$10 Prodution Chairs -90 40 90 $C$10 Prodution Tables 60 220 60 33.33 $D$10 Prodution Bookcases 40 280 50 60 Constraints Final Shadow Constraint Allowable Allowable R.H. Side Cell $E$5_Assembly (minutes) Total Used $E$6 Name Value Price Increase Decrease 3600 2000 3800 3600 4 200 600 Finishing (minutes) Total Used 2000 5 400 1E+30 400 SES7 Wood (pounds) Total Used 3600 For each of the following parts, answer the question as specifically and completely as is possible using just the sensitivity report, without re-solving the problem with the Solver. All problems are independent (i.e., any change made in one problem part does not apply for the other problem parts). Justify your answers by utilizing the results in the sensitivity report. a. Suppose the profit per bookcase decreases by $25. 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 $10 and the profit per bookcase increases by $40. 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 less hours are available in the assembly department. How much would this affect total profit? Would it change the optimal production quantities? 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 her time from the assembly department to the finishing department? Indicate the rate at which this would increase or decrease total profit per minute shifted. How many minutes can be shifted before this rate might change? e. The allowable decrease for the chairs variable cell and the allowable decrease for the wood constraint were both accidentally deleted from the sensitivity report. Based on the nature of the solution, you should be able to infer what numbers were there. For each, indicate what number should be there and, in a sentence or two, explain the intuition as to why you know that particular number should be there.

During the next production period, The Diego Garcia Furniture Company is considering producing dining room chairs, dining room tables and/or bookcases. Each item must go through the two stages of production (assembly and finishing), and requires a certain amount of wood (fine cherry wood). They have formulated a linear program to determine the production levels that would maximize profit. The solved spreadsheet model and corresponding sensitivity report are shown below. A B D E F G 1 Chairs Tables Bookcases 2 Unit Profit $40 $220 $280 3 4 Resources Required per Unit Total Used Available 5 Assembly (minutes) Finishing (minutes) Wood (pounds) 20 30 45 3600 く= 3600 10 20 20 2000 <= 2000 7 10 30 45 3600 く= 3800 8 9 Chairs Tables Bookcases Total Profit 10 Prodution 60 40 $24,400 Variable Cells Objective Coefficient Final Reduced Allowable Allowable Cell Name Value Cost Increase Decrease $B$10 Prodution Chairs -90 40 90 $C$10 Prodution Tables 60 220 60 33.33 $D$10 Prodution Bookcases 40 280 50 60 Constraints Final Shadow Constraint Allowable Allowable R.H. Side Cell $E$5_Assembly (minutes) Total Used $E$6 Name Value Price Increase Decrease 3600 2000 3800 3600 4 200 600 Finishing (minutes) Total Used 2000 5 400 1E+30 400 SES7 Wood (pounds) Total Used 3600 For each of the following parts, answer the question as specifically and completely as is possible using just the sensitivity report, without re-solving the problem with the Solver. All problems are independent (i.e., any change made in one problem part does not apply for the other problem parts). Justify your answers by utilizing the results in the sensitivity report. a. Suppose the profit per bookcase decreases by $25. 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 $10 and the profit per bookcase increases by $40. 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 less hours are available in the assembly department. How much would this affect total profit? Would it change the optimal production quantities? 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 her time from the assembly department to the finishing department? Indicate the rate at which this would increase or decrease total profit per minute shifted. How many minutes can be shifted before this rate might change? e. The allowable decrease for the chairs variable cell and the allowable decrease for the wood constraint were both accidentally deleted from the sensitivity report. Based on the nature of the solution, you should be able to infer what numbers were there. For each, indicate what number should be there and, in a sentence or two, explain the intuition as to why you know that particular number should be there.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 56P

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