As part of a weight reduction program a man designs a monthl

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 24 hours, devote at most 5 hours to swimming and jog for no more than the total number of hours bicycling and swimming. The calories burned per hour by bicycling, joging, and swimming are 200,595, and 295, respectively. How many hours should be alloted to each activity to maximize the number of calories burned? If he loses 1 pound of weight for each 3,500 calories burned.

How many hours should be alloted to each activity to maximize the number of calories burned?

____ hours for swimming

____ hours for bicycling

____ Hours for Jogging

How many pounds will he lose each month excercising?

____ Pounds

Solution

Ans:

B = Bicycling hours
J = Jogging hours
S = Swimming hours
R = Bicycling rate = 200 cal/h
Rj = Jogging rate = 595 cal/h
Rs = Swimming rate = 295 cal/h

       As , B + J + S 24

i.e, B + J + S = 24

As most hours = most calories burned

We would like to maximize J, since Rj is the highest rate however there are other constraints:
S 5and J B + S
To maximize J, we must maximize B + S
Since: S 5 and Rs > R, then S must be maximized. i.e. S= 5 hours
because swimming burns more calories compared to Bicycling.
So, J B + 5
J – B 5 since, Rj > R then (J – B) must be maximized
J – B = 5

J = B + 5
Again B + S + J = 24
B + 5 + (B + 5) = 24
2B + 10 = 24

So, B = 7 hours
      J = B + 5
      J = 7 + 5
    J = 12 hours and S = 5 hours

1. 5 hours for swimming

      2. 7 hour for bicycling

     3. 12 hours for Jogging

The maximum number of calories burned = 200B + 595J + 295S
= 200*7 + 595*12 + 295*5 = 10015 Calories.
He lose weight each month excercising = 10015/3500 = 2.861 Pound.