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 4.79

49. The maximum production of a soft-drink bottling company is 5000 cartons per day. The company produces regular and diet drinks and must make at least 600 cartons of regular and 1000 cartons of diet per day. Production costs are $1.00 per carton of regular and $1.20 per carton of diet. The daily operating budget is $5400. How many cartons of each type of drink should be produced if the profit is $0.10 per regular and $0.11 per diet? How, if at all, do the maximum profit and optimal bottling policy change if the company has no minimum required production?

49.

Make 3000 cartons of regular and 2000 cartons of diet in both cases.