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The Trim-Look Company makes a line of hand-made shirts, dresses, and coats for women. Each product must pass through the cutting and sewing department. In addition, each product makes use of the same polyester fabric. They have formulated a linear programming spreadsheet model to determine the production levels that would maximize profit. The spreadsheet model and sensitivity report are shown below. Answer the following questions as specifically and completely as is possible without re-solving the problem with Solver. Justify your answers using the results from the sensitivity report. All problems are independent (i.e., any change made in one part does not affect the other parts). Type your answers into a single worksheet tab on your spreadsheet, clearly labeling each answer (a, b, c, etc.). E F D. G Shirts Coats Dresses $30 Profit Per Unit $5 $20 3. 4 Resources Resources Required per Unit Produced Cutting (hours) Sewing (hours) Material (yards) 8. 9. Totals 200 Available 200 360 160 6 280 2 160 Shirts Dresses Coats Total Profit 10 Production 20 40 $1,400 Variable Cells Objective Coefficient 5. 30 Final Allowable Cell SBS10 Production Shirts SC$10 Production Dresses $D$10 Production Coats Reduced Cost -2.5 Allowable Increase 2.5 10 Name Value Decrease 1E+30 3.33 5 20 40 20 2.5 Constraints Final Shadow Constraint Allowable Allowable Cell SESS Cutting (hours) Totals SES6 Sewing (hours) Totals SES7 Material (yards) Totals Name Value Price R.H. Side 200 360 Increase 200 280 40 1E+30 Decrease 40 80 160 2.5 160 40 26.67 a. Suppose the profit per coat decreases to $18. Will this change the optimal production quantities? What can be said about the change in total profit? b. How much would the selling price of shirts need to be increased before it might become profitable to produce this product? c. Suppose the profit per dress increases by $7 and the profit per coat decreases by $3. Will this change the optimal production quantities? What can be said about the change in total profit?

The Trim-Look Company makes a line of hand-made shirts, dresses, and coats for women. Each product must pass through the cutting and sewing department. In addition, each product makes use of the same polyester fabric. They have formulated a linear programming spreadsheet model to determine the production levels that would maximize profit. The spreadsheet model and sensitivity report are shown below. Answer the following questions as specifically and completely as is possible without re-solving the problem with Solver. Justify your answers using the results from the sensitivity report. All problems are independent (i.e., any change made in one part does not affect the other parts). Type your answers into a single worksheet tab on your spreadsheet, clearly labeling each answer (a, b, c, etc.). E F D. G Shirts Coats Dresses $30 Profit Per Unit $5 $20 3. 4 Resources Resources Required per Unit Produced Cutting (hours) Sewing (hours) Material (yards) 8. 9. Totals 200 Available 200 360 160 6 280 2 160 Shirts Dresses Coats Total Profit 10 Production 20 40 $1,400 Variable Cells Objective Coefficient 5. 30 Final Allowable Cell SBS10 Production Shirts SC$10 Production Dresses $D$10 Production Coats Reduced Cost -2.5 Allowable Increase 2.5 10 Name Value Decrease 1E+30 3.33 5 20 40 20 2.5 Constraints Final Shadow Constraint Allowable Allowable Cell SESS Cutting (hours) Totals SES6 Sewing (hours) Totals SES7 Material (yards) Totals Name Value Price R.H. Side 200 360 Increase 200 280 40 1E+30 Decrease 40 80 160 2.5 160 40 26.67 a. Suppose the profit per coat decreases to $18. Will this change the optimal production quantities? What can be said about the change in total profit? b. How much would the selling price of shirts need to be increased before it might become profitable to produce this product? c. Suppose the profit per dress increases by $7 and the profit per coat decreases by $3. 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.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 71P
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Sensitivity Analysis for a Manufacturing Problem The Trim-Look Company makes a line of hand-made shirts, dresses, and coats for women. Each product must pass through the cutting and sewing department. In addition, each product makes use of the same polyester fabric. They have formulated a linear programming spreadsheet model to determine the production levels that would maximize profit. The spreadsheet model and sensitivity report are shown below. Answer the following questions as specifically and completely as is possible without re-solving the problem with Solver. Justify your answers using the results from the sensitivity report. All problems are independent (i.e., any change made in one part does not affect the other parts). Type your answers into a single worksheet tab on your spreadsheet, clearly labeling each answer (a, b, c, etc.). E F G D Shirts Dresses Coats Profit Per Unit $5 $30 $20 3 4 Resources Resources Required per Unit Produced Cutting (hours) Sewing (hours) Material (yards) Totals Available 5 200 200 6. 4 280 <= 360 7 2 160 160 <= 8 Shirts Dresses Coats Total Profit 10 Production $1,400 20 40 Variable Cells Final Reduced Objective Allowable Allowable Increase Cell Name Value Cost Coefficient Decrease $B$10 Production Shirts -2.5 2.5 10 1E+30 3.33 $C$10 Production Dresses 20 30 $D$10 Production Coats 40 20 2.5 5 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SES5 Cutting (hours) Totals SE$6 Sewing (hours) Totals SES7 Material (yards) Totals 200 200 40 40 280 360 1E+30 80 160 2.5 160 40 26.67 a. Suppose the profit per coat decreases to $18. Will this change the optimal production quantities? What can be said about the change in total profit? b. How much would the selling price of shirts need to be increased before it might become profitable to produce this product? c. Suppose the profit per dress increases by $7 and the profit per coat decreases by $3. Will this change the optimal production quantities? What can be said about the change in total profit?
Transcribed Image Text:Sensitivity Analysis for a Manufacturing Problem The Trim-Look Company makes a line of hand-made shirts, dresses, and coats for women. Each product must pass through the cutting and sewing department. In addition, each product makes use of the same polyester fabric. They have formulated a linear programming spreadsheet model to determine the production levels that would maximize profit. The spreadsheet model and sensitivity report are shown below. Answer the following questions as specifically and completely as is possible without re-solving the problem with Solver. Justify your answers using the results from the sensitivity report. All problems are independent (i.e., any change made in one part does not affect the other parts). Type your answers into a single worksheet tab on your spreadsheet, clearly labeling each answer (a, b, c, etc.). E F G D Shirts Dresses Coats Profit Per Unit $5 $30 $20 3 4 Resources Resources Required per Unit Produced Cutting (hours) Sewing (hours) Material (yards) Totals Available 5 200 200 6. 4 280 <= 360 7 2 160 160 <= 8 Shirts Dresses Coats Total Profit 10 Production $1,400 20 40 Variable Cells Final Reduced Objective Allowable Allowable Increase Cell Name Value Cost Coefficient Decrease $B$10 Production Shirts -2.5 2.5 10 1E+30 3.33 $C$10 Production Dresses 20 30 $D$10 Production Coats 40 20 2.5 5 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SES5 Cutting (hours) Totals SE$6 Sewing (hours) Totals SES7 Material (yards) Totals 200 200 40 40 280 360 1E+30 80 160 2.5 160 40 26.67 a. Suppose the profit per coat decreases to $18. Will this change the optimal production quantities? What can be said about the change in total profit? b. How much would the selling price of shirts need to be increased before it might become profitable to produce this product? c. Suppose the profit per dress increases by $7 and the profit per coat decreases by $3. Will this change the optimal production quantities? What can be said about the change in total profit?
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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
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