Jill 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

Question
Asked Oct 24, 2019
140 views

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

check_circle

Expert Answer

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:

maximize z 528r 492s 348w
subject to
rsw12......(1)
rs4..2)
w 3s..(3
help_outline

Image Transcriptionclose

maximize z 528r 492s 348w subject to rsw12......(1) rs4..2) w 3s..(3

fullscreen
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:

rs3s12
4 4s12
4s 8
S2
help_outline

Image Transcriptionclose

rs3s12 4 4s12 4s 8 S2

fullscreen
Step 3

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

...
w 3s
since, s 2
w 3(2)
w 6 hours
help_outline

Image Transcriptionclose

w 3s since, s 2 w 3(2) w 6 hours

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math