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 4.72

42. A clerk in a bookstore has 90 min at the end of each workday to process orders received by mail or on voice mail. The store has found that a typical mail order brings in a profit of $30 and a typical voice-mail order brings in a profit of $40. Each mail order takes 10 min to process and each voice-mail order takes 15 min. How many of each type of order should the clerk process? How, if at all, do the maximum profit and optimal processing policy change if the clerk must process at least three mail orders and two voice-mail orders?