Question

H-Town Plastics produces two models of plastic fan shrouds for the automotive industry. Model A is designed for low capacity radiators and Model B is designed for high capacity radiators. Both models require molding and assembly. Each Model A uses 2 minutes of molding and 8 minutes of assembly, and each Model B uses 6 minutes of molding and 4 minutes of assembly. There are 480 molding minutes available and 960 assembly minutes available for tomorrow’s production run. Each Model A contributes $23 to profits, and each Model B contributes $70 to profits. Use linear programming and the corner point graphical method to determine the product mix that will maximize profit for the next day of production.

a) Formulate (algebraically) this problem as a profit maximizing linear program. b) Solve this problem using the corner-point graphical method.

Answer 1

a)

Let

x = number of model A

y = number of model B

Formulation

Maximize 23x + 70y

Subject to

2x + 6y <= 480

8x + 4y <= 960

x, y >= 0

b)

The graph is shown below. The feasible region is covered by the dotted points. The corner points are shown. We have not marked the point (0, 0) as it will not be the maximizing function.

The objective function values at these points are

At (0, 80), 23*0 + 70*80 = 5600

At (96, 48), 23*96 + 70*48 = 5568

At (120, 0), 23*120 + 70*0 = 2760

The maximum value is at (0, 80). This means the optimum solution is to produce 0 units of model A and 80 units of model B. This will provide a profit of 5600