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 4040 hours, devote at most 33 hours to swimming, and jog for no more than the total number of hours bicycling and swimming. The calories burned per hour by bicycling, jogging, and swimming are 200, 473473, and 257257, 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?

Solution

Let the number of hours spent in bicycling be x₁, in joffing be x₂, in swimming be x₃.
Calories burnt in each are 200, 473473 and 257257 respectively

Objective Function: 200x₁+473473x₂+257257x₃

Constraints:
x₁+x₂+x₃ <=4040
x₃<=33
x₂<=x₁+x₃
x₁,x₂,x₃>=0

Putting all these in a solver, we get the following results:

x₁=1987 x₂=2020 x₃=33
Maximum number of calories burnt = 965302341