Prof Eliud

1. Solve the following linear programming model by using Microsoft Excel:
                  minimize Z = 3x₁ + 6x₂
                  subject to
                  7x₁ + 3x₂ ≥ 40
                  x₁, x₂ ≥ 0 and integer
2. A jeweler and her apprentice make silver pins and necklaces by hand. Each week, they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin and 10 hours of labor and 6 ounces of silver to make a necklace. Each pin also contains a small gem of some kind. The demand for pins is no more than six per week. A pin earns the jeweler $400 in profit, and a necklace earns $100. The jeweler wants to know how many of each item to make each week to maximize profit.
   1. Formulate an integer programming model for this problem.
      1. Solve the linear programming model that you formulated.
   2. Compare this solution with the solution without integer restrictions and indicate whether the rounded-down solution would have been optimal.

Submission Requirements:

• Submit your response in a Microsoft Excel workbook.
• Show the detailed steps that you performed to solve the problem.