A manufacturer sells two types of products. Product 1 is sold ata price of $50 per unit and product 2 at a price of $60 per unit.Three units of raw material and 1.5 labor hours are needed tomanufacture one unit of product 1. Six units of raw material and 2labor hours are needed to manufacture one unit of product 2. Theunit variable cost for product 1 is $30, and for product 2 is $20.A total of 15,000 units of raw material and 10,000 labor hours areavailable. If any product 1 is produced, a setup cost of $20,000 isincurred; if any product 2 is produced, a setup cost of $35,000 isincurred. Determine how to maximize the manufacturer’s profit.
a) What is the effective capacity for product 1 and product 2,respectively?
b) In the optimal solution, which product(s) will bemanufactured? What is the optimal production quantity? What is theoptimal profit?
