The owner of Blue Ridge Hot Tubs, Howie Jones, has asked for your assistance 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 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 2.8 (and the file Fig2-8.xlsm that accompanies this book) that dynamically updates the feasible region and optimal solution as 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. Click the Reset button in file Fig2-8.xlsm before answering each of the following questions.

1. In the optimal solution to this problem, how many pumps, hours of labor, and feet of tubing are being used?
2. 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 they should consider acquiring and by how much would this increase profit?
3. 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?
4. If the company could acquire more tubing, should they? Why or why not? If so, how much additional tubing should they consider acquiring and how much would this increase profit?
5. By how much would profit increase if the company could reduce the labor required to produce Aqua-Spas from 9 to 8 hours? From 8 to 7 hours? From 7 to 6 hours?
6. By how much would profit increase if the company could reduce the labor required to produce Hydro-Luxes from 6 to 5 hours? From 5 to 4 hours? From 4 to 3 hours?
7. How much would the optimal profit change if the company increased the amount of tubing required to produce Aqua-Spas from 12 to 13 feet? From 13 to 14 feet? From 14 to 15 feet?
8. How much would the optimal profit change if the company increased the amount of tubing required to produce Hydro-Luxes from 16 to 17 feet? From 17 to 18 feet? From 18 to 19 feet?
9. By how much would the unit profit on Aqua-Spas have to change before the optimal product mix changes?
10. By how much would the unit profit on Hydro-Luxes have to change before the optimal product mix changes?

Figure 2.8: