A firm is engaged in the production of three types of products. The products earn profit of $3, $5 and $4 per unit respectively. Each product goes through three operations: cutting, sewing, and inspection. Each unit of the first product needs 12, 15 and 3 minutes in cutting, sewing and inspection respectively. Similarly, each unit of product 2 needs 10, 15 and 4 minutes and each unit of product 3 needs 8, 12 and 2 minutes respectively. During the next period, the firm has 300 hours of cutting, 300 hours of sewing, and 150 hours of inspection time available. The sales force requires that at least 1000 units of product 1 be produced next period. At least 20% total production must be in product type 3. (Hint: be careful of Minutes versus Hours)

Show the mathematical formulation Use solver to find the solution and the objective function value

Are we making money or losing money by producing Product 1?

Explain. Overtime in sewing department can be scheduled for $12 per hour.

Should we schedule overtime? If yes, how many hours? What will be the new profit?