A jeweler and her apprentice make silver pins as well as necklaces by hand. Each week they've 80 hours of labor and 36 ounces of silver available. It needs 8 hours of labor and 2 ounces of silver to make the pin, and 10 hours of labor and 6 ounces of silver to make necklace. Each pin also contains the small gem of some kind. The demand for pins is no more than 6 per week. A pin earns the jeweler $400 in profit, and necklace earns $100. The jeweler wants to know how many of each item to make each and every week to maximize profit.
a. Formulate integer programming model for this problem (written in format similar to the way Problems 1 and 2 were presented).
b. Solve this problem using the computer (note: if using QM for Windows, be sure to employ the Integer and Mixed Integer Programming Module).