The owner of Blue Ridge Hot Tubs, Howie Jones, has asked for your assistance in analyzing how the feasible region and solution to his production problem might change in response to changes in various parameters in the LP model. He is hoping that this might further his understanding of LP and how the constraints, objective function, and optimal solution interrelate. To assist in this process, he asked a consulting firm to develop the spreadsheet shown earlier in Figure (and the file Fig. on your data disk) that dynamically updates the feasible region and optimal solution and the various parameters in the model change. Unfortunately, Howie has not had much time to play around with this spreadsheet, so he has left it in your hands and asked you to use it to answer the following questions.

a. In the optimal solution to this problem, how many pumps, hours of labor, and feet of tubing are being used?

b. If the company could increase the number of pumps available, should they? Why or why not? And if so, what is the maximum number of additional pumps that they should consider acquiring, and by how much would this increase profit?

c. If the company could acquire more labor hours, should they? Why or why not? If so, how much additional labor should they consider acquiring and by how much would this increase profit?

d. If the company could acquire more tubing, should they? Why or why not? If so, how additional tubing should they consider acquiring and how much would this increase profit?

e. By how much would profit increase if the company could reduce the labor required to produce Aqua-Spas from 9 to 8 hours? And from 8 to 7 hours? And from 7 to 6 hours?

f. By how much would profit increase if the company could reduce the labor required to produce Hydro-Luxes from 6 to 5 hours? And from 5 to 4 hours? And from 4 to 3 hours?

g. By how much would profit increase if the company could reduce the amount of tubing required to produce Aqua-Spas from 12 to 11 feet? And from 11 to 10 feet? And from 10 to 9 feet?

h. By how much would profit increase if the company could reduce the amount of tubing required to produce Hydro-Luxes from 16 to 15 feet? And from 15 to 14 feet? And from 14 to 13 feet?

i. By how much would the unit profit on Aqua-Spas have to change before the optimal product mix changes?

j. By how much would the unit profit on Hydro-Luxes have to change before the optimal product mix changes?

Transcribed Image Text:

Fig2-8 xls (Compatibility Mode] - Microsoft Excel Home Insert Fage Layout Formulas Data Review View Add-Ins Blue Ridge Hot Tubs Aqua Spas Hydro Luxes X: (X) (X;) 250 Optimal Qty 122.00 78.00 225 $350 $300 Unit Profits 200 $66,100 Total Profit 175 Constraints # Required # Available 150 P Pumps 200 125- P Labor 1566 100 P Tubing 12 16 2880 75- Display 50 4 R Optimal solution P Profit level curve 25 P Pump boundary line P Labor boundary line P Tubing boundary line Reset 25 50 75 100 125 150 175 200 225 HIE Feasible region Ready 75%