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 4.75

45. A student has decided that passing a mathematics course will, in the long run, be twice as valuable as passing any other kind of course. The student estimates that passing a typical math course will require 12 hr a week to study and do homework. The student estimates that any other course will require only 8 hr a week. The student has 48 hr available for study per week. How many of each kind of course should the student take?

167

(Hint: The profit could be viewed as 2 “value points” for passing a math course and 1 “value point” for passing any other course.) How, if at all, do the maximum value and optimal course mix change if the student decides to take at least two math courses and two other courses?

Exercises 46–49 require finding the point of intersection of two lines, each corresponding to a resource constraint.