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 4.83

53. A rustic furniture company handcrafts chairs, tables, and beds. It has three workers, Chris, Sue, and Juan. Chris can work only 80 hr per month, but Sue and Juan can each put in 200 hr. Each of these artisans has special skills. To make a chair takes 1 hr of Chris’s time, 3 from Sue, and 2 from Juan. A table needs 3 hr from Chris, 5 from Sue, and 4 from Juan. A bed requires 5 hr from Chris, 4 from Sue, and 8 from Juan. Even artisans are concerned about maximizing their profit, so what product mix should the company stick with if it gets $100 profit per chair, $250 per table, and $350 per bed?

53.

Make 50 chairs, 10 tables, and no beds each month.