13 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 Xij 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?

Transcribed Image Text:

TABLE 13 Product Machine 1 Machine 2 Skilled Unskilled Sales ($) 1 11 4 8 2 7 34 6 5 654 5 4 6 7874 7 300 260 7 220 4 180