A cheese firm produces two types of cheese: Swiss cheese and sharp cheese. The firm has 60 experienced workers and would like to increase its working force to 90 workers during the next eight weeks. Each experienced worker can train 3 new employees in a period of two weeks during which the workers involved virtually produce nothing. It takes one hour to produce 10 pounds of Swiss cheese and one hour to produce 6 pounds of sharp cheese. A work week is 40 hours. The weekly demands (in 1000 pounds) are summarized below.
Cheese type Week
1 2 3 4 5 6 7 8
Swiss cheese 12 12 12 16 16 20 20 20
Sharp cheese 8 8 10 10 12 12 12 12
Suppose that a trainee receives full salary as an experienced worker. Further suppose that overaging destroys the flavor of the cheese so that inventory is limited to one week. How should the company hire and train its new employees so that the labor cost is minimized? Formulate the problem as a linear program.