solution

A company manufactures three products namely X, Y, and Z. Each of the products requires processing on three machines, Turning, Milling and Grinding. Product X requires 10 hours of turning, 5 hours of milling, and 1 hour of grinding. Product Y requires 5 hours of turning, 10 hours of milling, and 1 hour of grinding, and Product Z requires 2 hours of turning, 4 hours of milling, and 2 hours of grinding. In the coming planning period, 2700 hours of turning, 2200 hours of milling, and 500 hours of grinding are available. The profit contribution of X, Y, and Z are GH¢ 10, GH¢ 15, and GH¢ 20 per unit respectively. Find the optimal product mix to maximize the profit.

(a) Formulate a linear programming model for this problem.

(b) Use a solver to find the optimal solution and sensitivity report.