Question: 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. At present, Zales has 100 rubies, 120 sapphires, and 70 hours of jeweler ^' s labor. Extra rubies can be purchased at $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:

X1 = number of type 1 rings produced

X2 = number of type 2 rings produces

R = number of rubies purchased

Max 400 X1 +500 X2 -100R

s.t. 2X1+ 3X2- R \(\le \) 100

3X1+ 2X2 \(\le \) 120

X1+ 2X2 \(\le \) 70

X1 \(\ge \) 20

X2 \(\ge \) 25

R \(\ge \) 0

Solve this LP, and use the output to answer the following:

1. Suppose that instead of $100, each ruby costs $190. Would Zales still
   purchase rubies? What would the new optimal solution to the problem be?
2. Suppose that Zales were only required to produce at least 23 type 2 rings.
   What would Zale ^' s profit be now?
3. What is the most that Zales would be willing to pay for another hour of jeweler ^' s labor?
4. What is the most that Zales would be willing to pay for another sapphire?

Please enter the answer to part c.

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document