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 6 hours to swimming, and jog for no more than the total number of hours bicycling and swimming. The calories burned by this person per hour by bicycling, jogging, and swimming are 200, 591, and 269, 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? (Hint: Write the constraint involving jogging in the form 0.) Let x be the number of hours spent bicycling, let x2 be the number of hours spent jogging, and let x3 be the number of hours spent swimming. What is the objective function? z=0x1+x2+x3