4 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; type 2 sells for $500. All rings

produced by Zales can be sold. At present, Zales 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. To maximize profit, Zales should solve the following LP:
X1 = Type 1 rings produced X2 = Type 2 rings produced R2 = number of rubies purchased

Use the LINDO output in Figure 20 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 jeweler’s labor?
d What is the most that Zales would be willing to pay for another sapphire?

Transcribed Image Text:

LINDO Output for Vivian's Gem MAX 5 X1 +2 X2 SUBJECT TO 2) 3) 2 x1 4 X1 + X2