SHOW ALL WORK FOR LINEAR PROGRAMMING SOLUTION

Scott 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 company is struggling to hire competent workers for demand needs. 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 machine hour is limited to 3,000 hours a week and 1,500 hours is all that the company's labor force can offer. The steel beams require 150 hours of machine hours and 110 labor-hours. Wood beams require 140 machine hours and 70 labor 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)