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 34 hours, devote at most 7 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, 618, and 292, 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 x₁ 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 = 200 x₁ + 618 x₂ + 292 x3 To maximize the number of calories burned, the man should spend hours swimming. (Simplify your answers.) hours bicycling. hours jogging, and

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