Thor, a fitness trainer, has an exercise regimen that includes running, swimming

| August 30, 2017

1. Thor, a fitness trainer, has an exercise regimen that includes running, swimming, and walking. He has no more than 12 hours per week to devote to exercise, including at most 4 hours running. He wants to walk at least three times as many hours as he swims. Thor will burn on average 528 calories per hour running, 492 calories per hour swimming, and 348 calories per hour walking. Using Python, calculate how many hours per week Thor should spend on each exercise to maximize the number of calories he burns, as well as the maximum number of calories he will burn. (Hint: Write the constraint involving walking and swimming in the form ? 0.)

2. To be at his best as a teacher, Phil needs at least 10 units of vitamin A, 12 units of vitamin B, and 20 units of vitamin C per day. Pill #1 contains 4 units of A and 3 of B. Pill #2 contains 1 unit of A, 2 of B, and 4 of C. Pill #3 contains 10 units of A, 1 of B, and 5 of C. Pill #1 costs 6 cents, pill #2 costs 8 cents, and pill #3 costs 1 cent. How many of each pill must Phil take to minimize his cost?

3. A plant food is made from three chemicals, labeled I, II, and III. In each batch of the plant food, the amounts of chemicals II and III must be in the ratio of 5 to 3. The amount of nitrogen must be at least 29 kg. The percent of nitrogen in the three chemicals is 8%, 4%, and 5%, respectively. If the three chemicals cost $1.03, $0.83, and $0.68 per kilogram, respectively, how much of each should be used to minimize the cost of producing at least 650 kg of the plant food?

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