Exercises 40–51 each have several steps leading to a complete solution to a mixture problem. Practice a specific step of the solution algorithm by working out just that step for several problems. The steps are:

  1. Make a mixture chart for the problem.
  2. Using the mixture chart, write the profit formula and the resource- and minimum-constraint inequalities.
  3. Draw the feasible region for those constraints and find the coordinates of the corner points.
  4. Evaluate the profit information at the corner points to determine the production policy that best answers the question.
  5. (Requires technology) Compare your answer with the one you get from running the same problem on a simplex algorithm computer program.

Question 4.70

40. A clothing manufacturer has 600 yd of cloth available to make shirts and decorated vests. Each shirt requires 3 yd of material and provides a profit of $5. Each vest requires 2 yd of material and provides a profit of $2. The manufacturer wants to guarantee that under all circumstances, there are minimums of 100 shirts and 30 vests produced. How many of each garment should be made to maximize profit? If there are no minimum quantities, how, if at all, does the optimal production policy change?