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Social ScienceJill Sharp, a fitness trainer, has an exercise regimen that includes running, swimming, and walking. She has nomore than 12 hours per week to devote to exercise, including at most 4 hours running. She wants to walk atleast three times as many hours as she swims. Jill will burn on average 528 calories per hour running, 492calories per hour swimming, and 348 calories per hour walking. How many hours per week should Jill spendon each exercise to maximize the number of calories she burns? What is the maximum number of calories shewill burn? (Hint: Write the constraint involving walking and swimming in theform ? 0.)3
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
Expert Answer
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:
Image Transcriptionclose
maximize z 528r 492s 348w subject to rsw12......(1) rs4..2) w 3s..(3
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:
Image Transcriptionclose
rs3s12 4 4s12 4s 8 S2
So, jill can spend maximum of 2 hours on swimming to maximize the number of calories he burn.
...
Image Transcriptionclose
w 3s since, s 2 w 3(2) w 6 hours
Math
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