Chapter 4.4, Problem 33E

Calorie Expenditure Joe Vetere’s exercise regimen includes light calisthenics, swimming, and playing the drums. He has at most 10 hours per week to devote to these activities. He wants the total time he does calisthenics and plays the drums to be at least twice as long as he swims. His neighbors, however, will tolerate no more than 4 hours per week on the drums. According to a website, a 190-pound person like Joe will burn an average of 388 calories per hour doing calisthenics, 518 calories per hour swimming, and 345 calories per hour playing the drums. In Section 4.2, Exercise 36, Joe found that he could maximize calories burned in an exercise routine that did not include playing the drums as part of his exercise plan. Source: NutriStrategy.com.

1. (a) Joe really likes to play the drums and insists that his exercise plan include at least 1 hour of playing the drums per week. With this added constraint, now how many hours per week should Joe spend on each exercise to maximize the number of calories he burns? What is the maximum number of calories he will burn?
2. (b) Without the added constraint from part (a), Joe’s maximum calorie expenditure was $4313\frac{1}{3}$ calories. Compare this number with the new optimal solution. What conclusions can you draw when additional constraints are placed on a problem?
3. (c) Show how the solution from part (a) can be found without using the simplex method by considering the constraints and the number of calories for each activity.