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Formulate an Integer Programmming Model

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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 hour of labor and 6 ounces of silver to make a necklace. Each pin also contain a small gem of 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 want to know how many of each item to make each week to maximize profit.

a. Formulate an integer programmming mode for this problem
b. Solve this model using a computer.

Compare this solution with the solution without integer and indication where the rounded-down solution would have been optimal.

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