The artisans at Jewelry Junction in Phoenix are preparing to make gold jewelry during a 2-month period for the Christmas season. They can make bracelets, necklaces, and pins. Each bracelet requires 6.3 ounces of gold and 17 hours of labor, each necklace requires 3.9 ounces of gold and 10 hours of labor, and each pin requires 3.1 ounces of gold and 7 hours of labor. Jewelry Junction has available 125 ounces of gold and 320 hours of labor. A bracelet sells for $1,650, a necklace for $850, and a pin for $790. The store wants to know how many of each item to produce to maximize revenue.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer. Compare this solution with the solution with the integer restrictions relaxed and indicate whether the rounded-down solution would have been optimal.