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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.
Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during the next production cycle. Howie earns a profit of $350 on each Aqua-Spa he sells and $300 on each Hydro-Lux he sells. He is confident that he can sell all the hot tubs he produces. The question is, how many Aqua-Spas and Hydro-Luxes should Howie produce if he wants to maximize his profits during the next production cycle?
By how much would the unit profit on Hydro-Luxes have to change before the optimal product mix changes?
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Chapter 2 Solutions
Spreadsheet Modeling and Decision Analysis: A Practical Introduction to Business Analytics
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Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,