Chapter 2.CRE, Problem 45CRE

Production Scheduling Desmond Jewelry wishes to produce three types of pendants: Type A, Type B, and Type C. To manufacture a Type A pendant requires $2\text{min}$ on Machines I and II and $3\text{min}$ on Machine III. A Type B pendant requires $2\text{min}$ on Machine I, $3\text{min}$ on Machine II, and $4\min$ on Machine III. A Type C pendant requires $3\text{min}$ on Machine I, $4\text{min}$ on Machine II, and $3\text{min}$ on Machine III. There are $3\frac{1}{2}\text{hr}$ available on Machine I, $4\frac{1}{2}\text{hr}$ on Machine II, and $5\text{hr}$ available on Machine III. How many pendants of each type should Desmond make to use all the available time?