As part of a weight reduction programman designs a n of bicy

As part of a weight reduction program^man designs a n of bicycling, jogging, and swimming. He would like to d 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, jogging, and swimming are 200, 623, and 277, 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? How many hours should be allotted to each activity to maximize the number of calories burned? Hours for bicycling hours for jogging hours for swimming

Solution

let bycycling(x), jogging(y),swemming(z) are the hours spends by the problem x+y+z=36 the constraints arez<equal to 5 x+y< equal to31 y-x< equal to5solving the three inequalities we get three corners in the common shaded portion as (13,18),(0,5) (20,0) among them (13,18) gives the maximum loss of calories the answers are Total max calorie loss=200x+623y+277z=200x13+623x18+277x5=15199cal corresponding time spends are bycycling 13hrs,jogging 18hrs,swemmings5 hrs