Aldrin 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 sells for $500. All rings produced by Aldrin can be sold. Aldrin 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. a. Formulate this linear programming problem and solve it. b. Formulate the dual of this linear programming problem and solve it.