A small firm makes three similar products, which all follow the same three-step process, consisting of milling, inspection, and drilling. Product A requires 12 minutes of milling, 5 minutes for inspection, and 10 minutes of drilling per unit; Product B requires 10 minutes of milling, 4 minutes for inspection, and 8 minutes of drilling per unit; and product C requires 8 minutes of milling, 4 minutes for inspection and 16 minutes of drilling. The department has 20 hours available during the next period of milling, 15 hours for inspection and 24 hours for drilling. Product A contributes $2.40 per unit to profit, product B $2.50 per unit and product C $3 per unit. 1. Formulate the problem as a linear programming problem. Clearly state the decision variables, objective function and the constraints.
2. Can this problem be solved using graphical method? Explain why.
3. Solve the problem using Solver. Determine the optimum solution (how much of each product needs to be made), and the profit.