(a) Explanation Given: Ginger devotes 10 hours per week and her fencing partner can work with her at most 2 hours per week. A 130-pound person like Ginger will burn an average of 236 calories per hour doing tai chi, 295 calories per hour riding a unicycle, and 354 calories per hour in fencing. Explanation: Consider that a 130-pound person like Ginger will burn an average of 236 calories per hour doing tai chi, 295 calories per hour riding a unicycle, and 354 calories per hour in fencing. Ginger devotes 10 hours per week and her fencing partner can work with her at most 2 hours per week. Let x 1 be the number of hours doing tai chi, x 2 be the number of hours doing unicycling, and x 3 be the number of hours doing fencing. Maximize z = 236 x 1 + 295 x 2 + 354 x 3 Subject to x 1 + x 2 + x 3 ≤ 10 x 3 ≤ 2 − x 1 + 2 x 2 ≤ 0 with x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 First simplex tableau is [ x 1 x 2 x 3 s 1 s 2 s 3 z 1 1 1 1 0 0 0 10 0 0 1 0 1 0 0 1 − 1 2 0 0 0 1 0 0 − 236 − 295 − 354 0 0 0 1 0 ] Pivot 1 in column 3, row 2 R 1 → − R 2 + R 1 R 4 → R 4 + 354 R 2 Then [ x 1 x 2 x 3 s 1 s 2 s 3 z 1 1 1 1 − 1 0 0 8 0 0 0 0 − 1 0 0 2 − 1 2 2 0 0 1 0 0 − 236 − 295 − 295 0 354 0 1 708 ] Pivot 2 in row 3, column 2 R 1 → 2 R 1 − R 3 R 4 → 2 R 4 + 295 R 3 [ x 1 x 2 x 3 (b) To determine To show: How the solution from part (a) can be found without using the simplex method.

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 4, Problem 47RE

(a)

To determine

How many hours per week should Ginger spend on each activity to maximize the number of calories she burns, and the maximum value of calories that she will burn.

(b)

To determine

To show: How the solution from part (a) can be found without using the simplex method.

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Chapter 4, Problem 46RE

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How many hours per week should Ginger spend on each activity to maximize the number of calories she burns, and the maximum value of calories that she will burn.

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How many hours per week should Ginger spend on each activity to maximize the number of calories she burns, and the maximum value of calories that she will burn.

To show: How the solution from part (a) can be found without using the simplex method.

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