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 4.85

55. A gourmet coffee distributor has on hand 17,600 lb of African coffee, 21,120 oz of Brazilian coffee, and 12,320 oz of Colombian coffee. It sells four blends—Excellent, Southern, World, and Special—on which it makes these per-pound profits, respectively: $1.80, $1.40, $1.20, and $1.00. One pound of Excellent is 16 oz of Colombian; it is not a blend at all. One pound of Southern consists of 12 oz of Brazilian and 4 oz of Colombian. One pound of World requires 6 oz of African, 8 oz of Brazilian, and 2 oz of Colombian. One pound of Special is made up of 10 oz of African and 6 oz of Brazilian. What product mix should the gourmet coffee distributor prepare to maximize profit?

55.

Make 470 pounds of Excellent, none of Southern, 2400 pounds of World, and 320 pounds of Special.