Joe Vetere's exercise regime includes light calisthenics, swimming, and playing drums. He has at most 10 hrs 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 4hrs per week on the drums. According to the website, a 190lb person like Joe will burn an average of 388 calories per hr doing calisthenics, 518 calories per hr swimming, and 345 calories per hr playing drums.
a) Joe really likes to play drums and insists that his exercise plan include at least 1 hr of playing drums per week. With this added constraint, now how many hrs per week could Joe spend on each exercise to maximize calories burned? What is the maximum calories he will burn?
b) Without the added constraint from part a, Joe's maximum calories expenditure was 4313.333333 calories. Compare this number with the new optimal solution. What conclusions can you draw when additional constraints are placed on a problem?
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.
a) Joe really likes to play drums and insists that his exercise plan include at least 1 hr of playing drums per week. With this added constraint, now how many hrs per week could Joe spend on each exercise to maximize calories burned? What is the maximum calories he will burn?
b) Without the added constraint from part a, Joe's maximum calories expenditure was 4313.333333 calories. Compare this number with the new optimal solution. What conclusions can you draw when additional constraints are placed on a problem?
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.
