16 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 jeweler’s labor?
d What is 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?

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LINDO Output for Wheat/Corn (Problem 12) MAX 150A1+200A2-10L ST A1+A2 <45 6A1+10A2-L <0 L <350 5A1-140 4A2 <120 END LP OPTIMUM FOUND AT STEP 4 OBJECTIVE FUNCTION VALUE 1) 4250.000 VARIABLE VALUE Al 25.000000 A2 20.000000 L 350.000000 REDUCED COST 0.000000 0.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 75.000000 3) 0.000000 12.500000 4) 0.000000 2.500000 5) 15.000000 0.000000 6) 40.000000 0.000000 NO. ITERATIONS= 4 RANGES IN WHICH THE BASIS IS UNCHANGED: VARIABLE OBJ COEFFICIENT RANGES CURRENT ALLOWABLE ALLOWABLE INCREASE DECREASE 150.000000 10.000000 30.000000 COEF A1 A2 200.000000 L 50.000000 10.000000 2.500000 -10.000000 INFINITY RIGHTHAND SIDE RANGES CURRENT ALLOWABLE ALLOWABLE INCREASE DECREASE ROW RHS 2 45.000000 1.200000 6.666667 3 0.000000 40.000000 12.000000 4 350.000000 40.000000 12.000000 5 140.000000 INFINITY 15.000000 6 120.000000 INFINITY 40.000000