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 4.77

47. A paper recycling company uses scrap cloth and scrap paper to make two different grades of recycled paper. A single batch of grade A recycled paper is made from 25 lb of scrap cloth and 10 lb of scrap paper, whereas one batch of grade B recycled paper is made from 10 lb of scrap cloth and 20 lb of scrap paper. The company has 100 lb of scrap cloth and 120 lb of scrap paper on hand. A batch of grade A paper brings a profit of $500, whereas a batch of grade B paper brings a profit of $250. What amounts of each grade should be made? How, if at all, do the maximum profit and optimal production policy change if the company is required to produce at least one batch of each type?

image

47.

Make two grade A and five grade B batches in both cases.