University Ceramics manufactures plates, mugs, and steins, with their unit profit being $3.10, $4.75, and $4.00, respectively. The product input requirements and their supply are given in the table below.
University Ceramics
|
Product Input Requirements |
Supply Available |
| Plates |
Mugs |
Steins |
| P |
M |
S |
| Molding (min) |
4 |
6 |
3 |
2400 |
| Finishing (min) |
8 |
14 |
12 |
7200 |
| Clay (oz) |
5 |
4 |
3 |
3000 |
| Unit Profit |
$ 3.10 |
$ 4.75 |
$ 4.00 |
|
1. Solve the LP model for University Ceramics and create the Sensitivity Report. Upload the results into ACE. Use the results to answer the following questions. Each question should be answered independently.
2. How many of each product should University Ceramics make? What is the profit?
3. For any product type that is not scheduled to be produced what profit would be needed to induce the product to be produced?
4. Which constraints are binding and which have slack? For any with slack, indicate how much the slack is.
5. Suppose the profit per plate decreases from $3.10 to $2.80. Will this change the optimal production quantities? Why? What can be said about the change in total profits?
6. Suppose the profit per stein increases by $0.30 and the profit per plate decreases by $0.25. Will this change the optimal production quantities? Why? What can be said about the change in total profits?
7. Suppose a worker in the molding department calls in sick. Now eight fewer hours are available that day in the molding department. How much would this affect total profits? Would it change the optimal production quantities? Explain.
8. Suppose one of the workers in the molding department is also trained to do finishing. Would it be a good idea to have this worker shift some of her time from the molding department to the finishing department? Indicate the rate at which this would increase or decrease total profit per minute shifted. How many minutes can be shifted before this rate might change?
9. Suppose University Ceramics decides to polish each product prior to shipping. The process would require 12, 10, and 15 minutes, respectively, for plates, mugs, and steins. Would this change the current production plan if 145 hours of polishing time were available? Explain.
10. Suppose University Ceramics is considering the production of a fourth product, bowls (B). Bowls requires 6 minutes of molding time, 12 minutes of sewing time, and 6 ounces of clay. At what profit per bowl would this product be economically attractive to manufacture?
Explain. How many bowls can be made at this profit?