A company needs two parts, A and B, for its product. It can either buy them from another company, or can make them in its own plant, or do both. The costs of each alternative and the in-house production rates are as follows:

Part A Part B

Make $1.00/unit $2.00/unit

Buy $1.20/unit $1.50/unit

In-house production rate 3 units/h 5 units/h

The company must have at least 100 units of part A and 200 units of part B each week. There are 40 h of production time per week and idle time on the machine costs $3.00/h. Furthermore, no more than 60 units of A can be made each week, and no more than 120 units of B can be made each week. Also, no more than 150 units of B can be bought per week.

The company wants to determine an optimal plan which will minimize the total costs per week. Formulate this as a linear programming problem and solve. What is the optimal make or buy plan for the company?