Application and Reasoning Problems

16.6. Consider the situation described in #1 above. Under the stated conditions, the maximum profit of $192 per shift comes from making 16 Widgets and 12 Greebles. The following questions relate to the way the optimal solution changes under different conditions in the environment. Open file C16 Problem6.xls [.rda]. The problem has been set up for you, and the constraints and settings for Solver are already configured.

1. Suppose one of your work crews finds a way to cut the time for making the Greebles on machine I. Instead of needing 13 minutes, they need only 12 minutes on machine I. See the screen shot below for what this might look like in Excel. Notice that you now have enough time left to make either one more Widget or one more Greeble. Which would be better? Why?

16.7. Open file C16 Problem6.xls [.rda]. The problem has been set up for you, and the constraints and settings for Solver are already configured. Use Solver to help you explore the following change to the situation: Suppose the materials costs for Widgets are expected to increase. This will reduce your profit on each Widget. At what point should we drastically cut back on Widget production? At what point should we cut Widget production altogether?

16.8. Consider the situation described in #2 above. Under the given conditions, the optimal solution is shown in figure 16.13. Data file C16 Problem7.xls [.rda] has this problem set up for you, including the solver table constraints.

1. Given the current optimal solution, how many additional cabins of each type could be rented for the cruise?
2. Suppose the cost for operating the Corvettes is expected to increase. At what point should Harbor Tours supply Glacier Travel Agency with only Cruisers?

16.9. The file C16 Problem8.xls [.rda] shows the set up for the optimization problem below. C-Vite Company has decided to introduce three fruit juices made from blending two or more concentrates. These juices will be packaged in 2-qt (64 fluid oz) cartons. To make one carton of pineapple-orange juice requires 8 oz each of pineapple and orange juice concentrates. To make one carton of orange-guava juice requires 4 oz of guava concentrate and 12 oz of orange concentrate. Finally, to make one carton of pineapple-orange-guava juice requires 4 oz of pineapple juice concentrate, 4 oz of orange juice concentrate and 8 oz of guava juice concentrate. The company has decided to allot 22,000 oz of pineapple juice concentrate, 28,000 oz of orange juice concentrate and 12,000 oz of guava juice concentrate for the initial product run. The company also stipulated that the production of the pineapple-orange-guava juice should not exceed 900 cartons. Its profit on one carton of pineapple-orange juice is $1.00; its profits on one carton of orange-guava juice is $0.90; and its profit on one carton of pineapple-orange-guava is $0.95.

1. Explain how the spreadsheet sets up this problem for solution. Point out any unnecessary information provided in the problem statement (such unnecessary items are often called ”red herrings”.)
2. Find the optimal solution using Solver.
3. C-Vite is worried about a bad winter which could damage much of the Florida orange crop. If C-Vite only has 20,000 oz of orange juice concentrate to allot for the blends, how does this change their optimal production plan?
4. After a taste test, C-Vite decides to change the blend in the Pineapple-Orange-Guava juice to 4 oz pineapple, 6 oz orange and 6 oz guava. What optimal product mix should they pursue?

16.10. Oregon Lumber has decided to enter the pre-fabricated housing market. For its initial venture, it plans to offer three models of homes: traditional, deluxe and luxury. Each house is prefabricated and partially assembled at the factory. The final completion of the home takes place on site. The table below shows the costs, in material and labor, and the profit from each type of home.

During the first year, Oregon Lumber has $9 million to spend on materials. They cannot exceed 230,000 hours of labor in the factory, and they cannot exceed 245,000 hours of labor on site. Assuming that the market can sell as many houses as Oregon Lumber makes, how many of each type should be made if they want to maximize their profit?