The Alpine Sports Company makes a line of winter sports equipment, including skis, snowboards, and sleds. Each product uses time on an extruder machine and requires time in final assembly. In addition, each product is largely made of fiberglass. 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 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). В D E F G H 1 Alpine Sports Skis (pair) $90 Snowboard Sled 4 Profit Per Unit $140 $110 5 6 Resources Resources Required per Unit Produced Totals Available Extruder (minutes) Final Assembly (minutes) Fiberglass (pounds) 7 8 4 4 7200 7200 8 10 12 8 12780 <= 14400 4 12 15 9000 <= 9000 10 11 Skis (pair) Snowboard Sled Total Profit 12 Production 630 540 $132,300 Variable Cells Reduced Allowable Increase Final Objective Coefficient Allowable Cell Name Value Cost Decrease Production Skis (pair) 90 $C$12 $D$12 $E$12 630 190 43.33 Production Snowboard Production Sled 540 140 130 45 -58.5 110 58.5 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$7 $F$8 $F$9 Extruder (minutes) Totals Final Assembly (minutes) Totals 12780 Fiberglass (pounds) Totals 1800 1E+30 2314.29 7200 6.5 7200 4200 14400 9000 1620 9000 9.5 5400 a. Suppose the profit per snowboard decreases from $140 to $120. 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 sleds need to be increased before it might become profitable to produce this product? c. Suppose the profit per pair of skis increases by $45 and the profit per snowboard decreases by $40. Will this change the optimal production quantities? What can be said about the change in

The Alpine Sports Company makes a line of winter sports equipment, including skis, snowboards, and sleds. Each product uses time on an extruder machine and requires time in final assembly. In addition, each product is largely made of fiberglass. 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 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). В D E F G H 1 Alpine Sports Skis (pair) $90 Snowboard Sled 4 Profit Per Unit $140 $110 5 6 Resources Resources Required per Unit Produced Totals Available Extruder (minutes) Final Assembly (minutes) Fiberglass (pounds) 7 8 4 4 7200 7200 8 10 12 8 12780 <= 14400 4 12 15 9000 <= 9000 10 11 Skis (pair) Snowboard Sled Total Profit 12 Production 630 540 $132,300 Variable Cells Reduced Allowable Increase Final Objective Coefficient Allowable Cell Name Value Cost Decrease Production Skis (pair) 90 $C$12 $D$12 $E$12 630 190 43.33 Production Snowboard Production Sled 540 140 130 45 -58.5 110 58.5 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$7 $F$8 $F$9 Extruder (minutes) Totals Final Assembly (minutes) Totals 12780 Fiberglass (pounds) Totals 1800 1E+30 2314.29 7200 6.5 7200 4200 14400 9000 1620 9000 9.5 5400 a. Suppose the profit per snowboard decreases from $140 to $120. 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 sleds need to be increased before it might become profitable to produce this product? c. Suppose the profit per pair of skis increases by $45 and the profit per snowboard decreases by $40. Will this change the optimal production quantities? What can be said about the change in

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 73P

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