A small furniture manufacturer produces four products. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. The assembly time, finishing time, and inspection time for each unit of each product are provided in the table below. The unit cost, selling price, and the minimum demand for each product are also provided.
| Product 1 | Product 2 | Product 3 | Product 4 | Available Hours | |
| Assembly Time | 2.5 | 2 | 3 | 3.5 | 1200 |
| Finishing time | 2 | 1 | 1.5 | 2 | 880 |
| Inspection time | 0.5 | 1 | 0.5 | 1 | 400 |
| Cost per unit | $73 | $62 | $54 | $48 | |
| Selling Price | $264 | $244 | $248 | $230 | |
| The minimum demands (units) | 35 | 60 | 45 | 80 |
To keep a balance, the number of product 4 units at most twice the number of product 2 units.
1) Formulate a linear programming model for this problem. Clearly define the variables, objective function, and constraints.
2) Solve the problem using Excel and answer the following questions:
a) What is the optimal solution to this LP problem?
b) Would the optimal solution change if the Selling Price of Product 4 increases by $80 and all other Products are unchanged? Explain.
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