California Cabinets manufactures outdoor tables the company sells to local dealers throughout the Southwest. Because of an increase in demand for its products, California Cabinets is considering hiring subcontractors to complete its current backlog of orders. The following information is available for each subcontractor: Subcontractor 1 Subcontractor 2 Subcontractor 3 Hours required to complete wood tables 50 42 30 Hours required to complete steel tables 60 48 35 Hours available 40 30 35 Cost per hour $36 $42 $55 For example, Subcontractor 1 estimates it will take 50 hours to complete all wood tables and 60 hours to complete all steel tables. However, Subcontractor 1 only has 40 hours available. Therefore, Subcontractor 1 can only complete 40/50 = .80 or 80% of the wood tables if the company worked only on the wood tables or 40/60 = .67 or 67% if it worked only on the steel tables.
Formulate a linear programming model you can use to determine the percentage of wood tables and the percentage of steel tables that should be assigned to each of the three subcontractors to minimize the total cost of completing both projects.
Solve the model from Part 1. What percentage of the wood tables and what percentage of the steel tables should be assigned to each subcontractor?
Based on your model, what is the total cost of completing both projects?
Suppose Subcontractor 2 reduced its costs to $38 per hour. What effect would this change have on the optimal solution? Explain.