A company has three machines to make units of A. Input and output data for 1 hr of operation of each machine are follows:

The company must produce 2000 units of A weekly. The company can purchase up to 1 ton of the raw material for $4/1b from one source and an unlimited amount from another source for $5.50/1b. The firm has 900 hr of labor available at $8/hr, and an additional 200 hr of overtime available at $12/hr. The company pays only for the labor and raw material it uses. How many hours should each machine be used to meet demands at minimum cost?

Machine 1 Machine 2 Machine 3 Input Raw Material (lb) 80 50 76 Labor (worker-hours) 16 35 33 Output (units of A) 37 43 52