Question

A retailer stocks four different types of umbrellas: women's, golf, men's and folding. The retailer wants to determine how many of each type of umbrella to stock to maximize profit. The retailer has constraints on the storage space, special display racks, demand and a marketing restriction. The retailer has constructed a linear program and generated the following sensitivity analysis report: Variable Cells Allowable Final Reduced Objective Allowable Decrease Coefficient Increase Value Cost Name 1E+30 -5.4 5.4 Women's 6.75 1E+30 12 Golf 1.142857143 1E+30 2 44 Men's 2.285714286 1E+30 Folding 13 4 Constraints Allowable Final Shadow Constraint Allowable Decrease R.H. Side. Increase Name Value Price 1E+30 1 Storage Space 89 Special Display 45 90 30 1.25 3.2 45 Racks 44 Demand 50 1 50 2 Marketing Restrictions 2.142857143 15 -3.2 15 1 How many women's umbrellas.chould be stocked2 (Enter vour ancwer in o o c 1. How many women's umbrellas should be stocked? (Enter your answer in blank #1.) 2. How many golf umbrellas should be stocked? (Enter your answer in blank # 2.) 3. How many men's umbrellas should be stocked? (Enter your answer in blank #3.) 4. How many folding umbrellas should be stocked? (Enter your answer in blank #4.) 5. What is the maximum profit? (Enter your answer in blank #5.) 6. How much storage space is left unused? (Enter your answer in blank #6.) 7. How many racks 8. By how much is the marketing restriction exceeded? (Enter your answer in blank #8.) 9. By how much can the profit on women's umbrella increase before the solution would change? (Enter your answer in blank # 9.) 10. To what value can the profit would change? (Enter your answer in blank #10.) 11. By how much can the demand decrease before there is a change in the optimal solution? (Enter your answer in blank #11.) 12. Suppose the marketing restriction increases to 20. What is the new maximum profit? (Enter your answer in blank #12.) 13. You are offered an additional display rack at a cost of $20. Would you say yes or no? (Enter your answer in blank #13. ) 14. Suppose the store plans to decrease the display racks to 35. What is the new maximum profit? (Enter your answer in blank #14.) are used? (Enter your answer in blank #7.) golf umbrellas decrease before the solution on

Answer 1

1. The stock of women umbrella can be found from the first table which shows the final value as 0 so, there should be zero stock of women's umbrella

2. Golf umbrellas are having final value 12 so, 12 golf umbrella should be stocked

3. 44 men's umbrella should be stocked

4. 13 folding umbrellas should be stocked

5. Maximum profit can be found by multiplying objective coefficient with the final values

=5*0+8*12+2*44+4*13= 236

6. Storage space final value is 89 and the RHS is 90 so left unused= 90-89=1

7. Racks final value is 45 so racks used is 45

8. Marketing restriction RHS is 15 and final value is 15 so exceeding value = 15-15=0

9. Allowable increase in profit of women's umbrella = 5.4

10 Allowable decrease for Golf umbrella is 6.75 so the final value can be 8-6.75=1.25 before changing the solution.

11. Demand allowable decrease = 44 units

12. Allowable increase of market restrictions os 5 so it can go to 15+5=20 so there will no change in profit for 20 marketing restriction

13. The allowable increase of display rack is 1.25 so getting another will not change the maximum profit hence we should say no to the new rack by spending $20

14. Allowable decrease in display rack is  30 which won't change the maximum profit when it becomes 35.

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