In Exercises 52–55, there are more than two products in the problem. Although you cannot solve these problems using the two-dimensional graphical method, you can follow these steps:

  1. Make a mixture chart for each problem.
  2. Using the mixture chart, write the resource- and minimum-constraint inequalities. Also write the profit formula.
  3. (Requires software) If you have a simplex method program available, run the program to obtain the optimal production policy.

Question 4.82

52. A toy company makes three types of toys, each of which must be processed by three machines: a shaper, a smoother, and a painter. Each Toy A requires 1 hr in the shaper, 2 hr in the smoother, and 1 hr in the painter, and brings in a $4 profit. Each Toy B requires 2 hr in the shaper, 1 hr in the smoother, and 3 hr in the painter, and brings in a $5 profit. Each Toy C requires 3 hr in the shaper, 2 hr in the smoother, and 1 hr in the painter, and brings in a $9 profit. The shaper can work at most 50 hr per week, the smoother 40 hr, and the painter 60 hr. What production policy would maximize the toy company’s profit?