A small firm makes three products which all follow the same

A small firm makes three products, which all follow the same three-step process, which consists of milling, inspection, and drilling. Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $6.00 per unit to profit, product B contributes $4.00 per unit, and product C contributes $10.00 per unit. What is the optimum mix of products in terms of maximizing contributions to profits?

Formulate a LP Model for this problem

Solution

In this there are three variable (A,B,C) and three constraints( milling, inspection, drilling).

For consists of milling

6A+2.5B+5C<=1200

For consists of inspection

5A+2B+4C<=900

For consists of drilling

4A+2B+8C<=1440

the maximize function is

6A+4B+10C

Using Excel

The optimum product mix is 180 units of B and 135 units of C, with an objective function value of 2,070.