As part of a training program, a man designs a monthly exercise program consisting of bicycling, jogging, and swimming. He would like to exercise at most 30 hours, devote at most 4 hours to swimming, and jog no more than the total number of hours bicycling and swimming. The calories burned per hour by bicycling, jogging, and swimming are 200, 475, and 275, respectively. How many hours should be allotted to each activity to maximize the number of calories burned? (a) Define variables for modeling this scenario, and write down the objective function. (b) Identify the constraints of the problem. (c) Write down the initial tableau for this problem. (Make sure to include the active variables). (d) How many hours should be allotted to each activity to maximize the number of calories burned? (As implied, solve this problem using the simplex method.)
As part of a training program, a man designs a monthly exercise program consisting of bicycling, jogging, and swimming. He would like to exercise at most 30 hours, devote at most 4 hours to swimming, and jog no more than the total number of hours bicycling and swimming. The calories burned per hour by bicycling, jogging, and swimming are 200, 475, and 275, respectively. How many hours should be allotted to each activity to maximize the number of calories burned?
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(a) Define variables for modeling this scenario, and write down the objective function.
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(b) Identify the constraints of the problem.
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(c) Write down the initial tableau for this problem. (Make sure to include the active variables).
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(d) How many hours should be allotted to each activity to maximize the number of calories burned? (As implied, solve this problem using the simplex method.)
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