Question

1. A firm produces four products: Each unit of product 1 requires two hours of assembly, one hour of painting and $50 of inventory, Each unit of product 2 requires one hour of assembly, three hours of painting and $75 of inventory, Each unit of product 3 requires 2.5 hours of assembly, 2.5 hours of painting and $20 of inventory, Each unit of product 4 requires 5 hours of assembly no painting and $100 of inventory. The firm has 140 hours of assembly time and 200 hours of painting time available. They also can not have more than $100,000 tied up in inventory. Each unit of product 1 returns a profit of $40, each unit of product 2 returns $30, each unit of product 3 returns $37 and each unit of product 4 returns $25. Not more than 20,000 units of product 1 can be sold, not more than 16,000 units of product 3 can be sold and there are no limits on the sale of products 2 and 4. We must however produce a minimum of 15,000 units of product 4 to fulfill a Gov. Contract. Formulate and LP model to maximize profit.

Answer 1