Question

Asked Oct 24, 2019

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Jill Sharp, a fitness trainer, has an exercise regimen that includes running, swimming, and walking. She has no

more than 12 hours per week to devote to exercise, including at most 4 hours running. She wants to walk at

least three times as many hours as she swims. Jill will burn on average 528 calories per hour running, 492

calories per hour swimming, and 348 calories per hour walking. How many hours per week should Jill spend

on each exercise to maximize the number of calories she burns? What is the maximum number of calories she

will burn? (Hint: Write the constraint involving walking and swimming in the

form ? 0.)

3

Step 1

According to the given information:

Let, **r be the number of hours jill spend on running **

**s be the number of hours jill spend on swimming**

**and, w be the number of hours jill spend on walking**

so, according to the question:

Step 2

Now solve the above equation to get the values of unknown:

From the second equation r≤4 means jill can spend maximum 4 hours for running so, jill will spend maximum of **4 hours on running** to maximize the number of calories he burn.

Therefore**, r=4**

Now, it is known that w=2s so equation 1 reduces to:

Step 3

So, jill can spend maximum of **2 hours on swimming** to maximize the number of calories he burn.

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