Question

Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows: Department Product 1 Product 2 Product 3 A 2.00 1.50 3.00 B 2.50 2.00 1.00 C 0.25 0.25 0.25 During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $30 for product 1, $25 for product 2, and $28 for product 3. Formulate a linear programming model for maximizing total profit contribution. If the constant is "1" it must be entered in the box. If required, round your answers to two decimal places. Let Pi = units of product i produced

Answer 1

Objective function:

Maximize Z: 30P1 + 25P2 + 28P3

Subject to: 2.00P1 + 1.50P2 + 3.00P3 ≤ 450 (Department A constraint)

2.50P1 + 2.00P2 + P3 ≤ 350 (Department B constraint)

0.25P1 + 0.25P2 + 0.25P3 ≤ 50 (Department C constraint)

P1, P2, P3 ≥ 0 (Non-negativity)

Step-by-step explanation:

The objective function is formulated from the contribution margin of the three products. For instance, the contribution of Product 1 is $30, the contribution of Product 2 is $25 and the contribution of Product 3 is $28. Thus, the objective function will be 30P1 + 25P2 + 28P3.

The constraints were obtained from the departmental labour hours requirements for each product. For instance, Product 1 requires 2 hours in department A, Product 2 requires 1.50 hours in department A and Product 3 requires 3 hours in Department A. Thus, the constraint will be 2.00P1 + 1.50P2 + 3.00P3.