Problem:
A company produces 4 different products, A, B, C, and D. All products require time in up to 5 different processing departments. The amount of time each product requires with each department is listed in the table below:
|
Product A |
Product B |
Product C |
Product D |
Available |
| Melting |
4 hrs |
1 hr |
2 hrs |
0 hrs |
250 hrs |
| Cooling |
2 hrs |
2 hrs |
0 hrs |
1 hr |
240 hrs |
| Shaping |
3 hrs |
2 hrs |
1 hr |
2 hrs |
220 hrs |
| Sanding |
0 hrs |
1 hr |
3 hrs |
3 hrs |
180 hrs |
| Painting |
1 hr |
2 hrs |
2 hrs |
1 hr |
250 hrs |
Suppose product A sells for $100/unit, product B sells for $125/unit, product C sells for $75/unit, and product D sells for $90/unit. And suppose that all products have a guaranteed buyer (i.e., no matter how many are produced it will be sold for the asking price). Management has asked for your recommendations about how many of each product type to produce that maximize revenue. Finally, you must produce at least 2 of each product.
Required:
Question 1) What is the formula for the Objective Function?
Question 2) What are the formulas for the Resource Constraints?
Question 3) What are the variable constraints?
Question 4) When you solve the Linear Program, what is the optimal number of each product?
Question 5) What is the optimal revenue?
Question 6) Which process (melting, cooling, etc) is there excess avaiable (slack)?
Question 7) Which process did you run out of?
Question 8) Submit an Excel Spreadsheet in which the Linear Progam is programmed and in which
Solve the given numerical problem and illustrate step by step calculation.