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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 20 ​hours, devote at most 7 hours to​ swimming, and jog for no more than the total number of hours cycling and swimming. The calories burned per hour by​ bicycling, jogging, and swimming are​ 200, 596​, and 294​, respectively. How many hours should be allotted to each activity to maximize the number of calories​ burned

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Answer:

Jogging = 10 hours

Swimming = 7 hours

Cycling = 3 hours

Step-by-step explanation:

J = Hours jogging

S = Hours swimming

C = Hours cycling

Since jogging is the activity that burns the most calories, we should maximize the number of hours jogging:

[tex]C+S+J = 20\\C+S=20-J\\J\leq C+S\\J\leq 20-J\\J\leq 10[/tex]

Therefore, the man should jog for 10 hours.

Since swimming is the activity that burns the second most calories, we should maximize swimming hours:

[tex]C+S=10\\S\leq 7\\S=7\\C=3[/tex]

In order to maximize the number of calories burn, the man should go jogging for 10 hours, swimming for 7 hours and cycling for 3 hours.

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