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Question 891730: I need help with this problem. I have come up with all the constraints I need to solve this with the simplex method except for her wanting to walk at least twice as many hours as she bikes. Rachel Reeve, a fitness trainer, has an exercise regimen that includes running, biking, and walking. She has no more than 15 hours a week to devote to exercise, including at mist 3 hours for running. She wants to walk at least twice as many hours as she bikes. A 130-pound person like Rachel will burn on average 531 calories per hour running, 472 calories per hour biking, and 354 calories per hour walking. How many hours per week should Rachel spend on each exercise to maximize the number of calories she burns? What is the maximum number of calories she will burn?
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! Whew! That's a convoluted problem, isn't it?
15 hours a week, with no more than 3 running.
Since running burns the most calories, she'll want to maximize that.
3 hours running at 531 cal = 1593 calories
That leaves 12 hours. Even though walking is the lowest calorie burner, she wants to walk 2x as often as biking. We'll want the minimum number of hours of walking in order to maximize calories.
12 = B + 2B (twice as many walking hours as biking)
12 = 3B
4 = B
4 hours biking * 472 cal = 1888 calories
If there are 4 hours biking, the minimum walking is 8 hours
8 hours walking * 354 cal = 2832 calories
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Total:
3 hours running at 531 cal = 1593 calories
4 hours biking * 472 cal = 1888 calories
8 hours walking * 354 cal = 2832 calories
Maximum amount of calories = 6313 calories in 15 hours
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