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
R = number of rubies purchased

Max z = 400X1 + 500X2 - 100R
SUBJECT TO
2) 2 X1 + 3 X2 - R <= 100
3) 3 X1 + 2 X2 <= 120
4) X1 + 2 X2 <= 70
5) X1 >= 20
6) X2 >= 25

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?