Question

Local Steel Construction Company produces two products, steel and wood beams. Steel beams have a unit contribution margin of $200, and wood beams have a unit contribution margin of $150. The demand for steel beams exceeds Local Steel Construction Company's production capacity, which is limited by available direct labor and machine-hours. The maximum demand for wood beams is 90 per week. Management desires that the product mix should maximize the weekly contribution toward fixed costs and profits.

Direct manufacturing labor is limited to 3,000 hours a week and 1,000 hours is all that the company's outdated machines can run a week. The steel beams require 120 hours of labor and 60 machine-hours. Wood beams require 150 labor hours and 120 machine-hours.

Required:

Formulate the objective function and constraints necessary to determine the optimal product mix. Solve for the optimal product mix. (Hint: note the non-negativity constraints)

Answer 1

Solution:

S = steel beams                 W = wood beams

Maximize:             $200 S + $150 W

Constraints:  Labor hours:          120 S + 150 W <3,000

Machine-hours:     60 S + 120 W<1,000

Wood beams:        W <90

                              W >0

Steel beams:          S >0