As part of a weight reduction program, a man designs a monthly exercise program consisting of bicycling, jogging, and swimming. He would like to exercise at most 36 hours, devote at most 4 hours to swimming, and jog for no more than the total number of hours bicycling and swimming. The calories burned by this person per hour by bicycling, jogging, and swimming are 200, 694, and 256, respectively. How many hours should be allotted to each activity to maximize the number of calories burned? What is the maximum number of calories he will burn? (Hint: Write the constraint involving jogging in the form ≤0.)
As part of a weight reduction program, a man designs a monthly exercise program consisting of bicycling, jogging, and swimming. He would like to exercise at most 36 hours, devote at most 4 hours to swimming, and jog for no more than the total number of hours bicycling and swimming. The calories burned by this person per hour by bicycling, jogging, and swimming are 200, 694, and 256, respectively. How many hours should be allotted to each activity to maximize the number of calories burned? What is the maximum number of calories he will burn? (Hint: Write the constraint involving jogging in the form ≤0.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:As part of a weight reduction program, a man designs a monthly exercise program consisting of bicycling, jogging, and
swimming. He would like to exercise at most 36 hours, devote at most 4 hours to swimming, and jog for no more than
the total number of hours bicycling and swimming. The calories burned by this person per hour by bicycling, jogging, and
swimming are 200, 694, and 256, respectively. How many hours should be allotted to each activity to maximize the
number of calories burned? What is the maximum number of calories he will burn? (Hint: Write the constraint involving
jogging in the form ≤0.)
Let x, be the number of hours spent bicycling, let x₂ be the number of hours spent jogging, and let x3 be the number of
hours spent swimming. What is the objective function?
z = x₁ + x₂ + x3
22/11
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