dolution

A company produces tools at two plants and sells them to three customers. The cost of producing 1,000 tools at a plant and shipping them to a customer is given in Table 14. Customers 1 and 3 pay $200 per thousand tools; customer 2 pays $150 per thousand tools. To produce 1,000 tools at plant 1, 200 hours of labor are needed, while 300 hours are needed at plant 2. A total of 5,500 hours of labor are available for use at the two plants. Additional labor hours can be purchased at $20 per labor hour. Plant 1 can produce up to 10,000 tools and plant 2, up to 12,000 tools. Demand by each customer is assumed unlimited. If we let X_ij = tools (in thousands) produced at plant i and shipped to customer

j then the company should solve the LP on the LINDO printout in Figure 23. Use this printout to answer the following questions:

a If it costs $70 to produce 1,000 tools at plant 1 and ship them to customer 1, what would be the new solution to the problem?

b If the price of an additional hour of labor were reduced to $4, would the company purchase any additional labor?

c A consultant offers to increase plant 1’s production capacity by 5,000 tools for a cost of $400. Should the company take her offer?

d If the company were given 5 extra hours of labor, what would its profit become?