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# Zales Jewelers uses rubies and sapphires to produce two

Zales Jewelers uses rubies and sapphires to produce two types of rings. A Type 1 ring requires 2 rubies, 3 sapphires, and 1 hour of jeweler's labor. A Type 2 ring requires 3 rubies, 2 sapphires. and 2 hours of jeweler's labor. Each Type 1 ring sells for $400, and each Type 2 ring sells for $500. All rings produced by Zales can be sold. Zales now has 100 rubies, 120 sapphires, and 70 hours of jeweler's labor. Extra rubies can be purchased at a cost of $100 per ruby. Market demand requires that the company produce at least 20 Type 1 rings and at least 25 Type 2 rings. To maximize profit, Zales should solve the following LP:

Use the LINDO output in Figure 14 to answer the following questions.

a. Suppose that instead of $ 100. each ruby costs $190 Would Zales still purchase rubies What would be the new optimal solution to the problem?

b. Suppose that Zales were only required to produce at least 23 Type 2 rings. What would Zales’ profit now be?

c. What is the most that Zales would be willing to pay for another hour of jewelers labor?

d. What ¡s the most that Zales would be willing to pay for another sapphire?

e. Zales is considering producing Type 3 rings Each Type 3 ring can be sold for $550 and requires 4 rubies. 2 sapphires, and 1 hour of jeweler’s labor, Should Zales produce any Type 3 rings?

FIGURE 14

UNDO Output for Jewelry

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