An athlete uses three different exercise regimens for increa

An athlete uses three different exercise regimens for increasing cardiovascular fitness. An

hour of regimen A rates a 3 in effectiveness, an hour of regimen B rates a 4 in effectiveness,

and an hour of regimen C rates a 5 in effectiveness. In any given week, the athlete can train

at most 3 hours by regimen A. In any given week the combined hours of regimens A and C

may not exceed 8. In any given week the combined hours of regimens B and C may not

exceed 11. How many hours of each regimen should the athlete perform in a week in order

to maximize the increase in fitness? What is the maximumvalue obtained??

Constraints aer

Number of hours of A <= 3

Number of hours of (A+B) <= 8

Number of hours of (B+C) <= 11

Maximize the objective function

Z = 3A + 4B + 5C

The maximum value will occur when the value of A is equal to 3 hours

then the value of B will be <= (8-3) = 5

then the value of C will be <= (11-5) = 6

Hence the maximum value will occur for doing 3 hours of activity A, 5 hours of activity B and 6 hours of activity C

Maximum value obtained

Z = 3 * 3 + 4 * 5 + 5 * 6

= 9 + 20 + 30

= 59 effectivness