Question: 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.

a. Formulate an integer programming model for this problem (written in a format similar to the way Problems 1 and 2 were presented).

b. Solve this problem by using the computer (note: if using QM for Windows, be sure to use the Integer and Mixed Integer Programming Module).