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Problema 1 (extraído y modificado del libro de texto, problema 5, página 232) Radioco manufactures two types of radios. The only scarce resource that is needed to produce radios is labor. At present, the company has two laborers. Laborer 1 is willing to work up to 40 hours per week and is paid \$5 per hour. Laborer 2 will work up to 50 hours per week for \$6 per hour. The price as well as the resources required to build each type of radio are given in Table 1. Letting xi be the number of Type i radios produced each week, Radioco should solve the following LP: Using the graphical solution: a For what values of the price of a Type 1 radio would the current basis remain optimal? b For what values of the price of a Type 2 radio would the current basis remain optimal? c If laborer 1 were willing to work only 30 hours per week, then would the current basis remain optimal? Find the new optimal solution to the LP. d If laborer 2 were willing to work up to 60 hours per week, then would the current basis remain optimal? Find the new optimal solution to the LP. e Find the shadow price of each constraint. Solucion:

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Problema 2 (extraído del libro de texto, problema 4, página 243) Gepbab Corporation produces three products at two different plants. The cost of producing a unit at each plant is shown in Table 6. Each plant can produce a total of 10,000 units. At least 6,000 units of product 1, at least 8,000 units of product 2, and at least 5,000 units of product 3 must be produced. To minimize the cost of meeting these demands, the following LP should be solved: Here, xij = number of units of product j produced at plant i. Use the LINDO output in Figure 9 to answer the following questions: a What would the cost of producing product 2 at plant 1 have to be for the firm to make this choice? b What would total cost be if plant 1 had 9,000 units of capacity?
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