Question

3. Integer Programming Problem (Chapter 6) A manufacturer can sell product 1 at a price of $30 per unit and product 2 at a price of $40 per unit. Three units of raw material and 1.5 labor hours are needed to manufacturer one unit of product 1. Six units of raw material and 2 labor hours are need to manufacture one unit of product 2. The unit variable cost for product 1 is $20, and for product 2 is $20. A total of 15,000 units of raw material and 8,000 labor hours are available. If any product 1 is produced, a setup cost of $15,000 is incurred; if any product 2 is produced, a setup cost of $35,000 is incurred. 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 be manufactured? What is the optimal production quantity? What is the optimal profit?

Answer 1

Sol a we have to find the effective capacity. Product a - We know Effective capacity for product - Material Available 1 = - - Raw material requined Pea unit 15 000 15900 Product 1 = 5000 unit Product 2 Effective capacity foa poduck, Material Available Raw material Deguised Pea unit 15000 15000 Baoduct 2 = 2,500 units profit ( excluding setup cost), If only Product 1 b). Gooss is produced . 5000+ (30-20) - 50oo – Clo) Gooss is produced - $50,000 profit, If only product 2 = 2500* (40-20) = 2500*20

product =$50,000 * oud gross profit from production of eithes of 1. is same * so wild produce only that product which has - set up cost visa. Product 1 with $ 15,000 less Our optimal solution * Boduct I should be * The optimad production s manufactured quantity will be 5,000 units * optimal profit generated i will be = 50,000 -15,000 = 35,000