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 4.81

51. Lights Aglow makes desk lamps and floor lamps, on which the profits are $2.65 and $4.67, respectively. The company has 1200 hr of labor and $4200 for materials each week. A desk lamp takes 0.8 hr of labor and $4 for materials; a floor lamp takes 1.0 hr of labor and $3 for materials. What production policy maximizes profit? How, if at all, do the maximum profit and optimal production policy change if Lights Aglow wants to produce at least 150 desk lamps and 200 floor lamps per week?

51.

Make no desk lamps and 1200 floor lamps; make 150 desk lamps and 1080 floor lamps.