Explanation Given: Lauren has at most 15 hours a week to exercise. She can’t run for more than 3 hours during the week and wants to at least twice as many hours as she bikes. She burns 531 calories per hour while running, 472 calories per hour while biking, and 354 calories per hour while walking. Explanation: Let the number of hours spent running, biking, and walking in the week be denoted by x , y and z, respectively. Let the number of calories she burns during the week be denoted by p . p = 531 x + 472 y + 354 z The restrictions she has can be represented by the following set of inequalities: x + y + z ≤ 15 x ≤ 3 z ≥ 2 y Also, the number of hours can’t be negative. This gives rise to three nonnegative constraints: x ≥ 0 , y ≥ 0 , z ≥ 0 This optimization problem can be written as Maximize p = 531 x + 472 y + 354 z Subject to x + y + z ≤ 15 x ≤ 3 2 y − z ≤ 0 with x ≥ 0 , y ≥ 0 , z ≥ 0 This can be solved using the Simplex method as follows: Add three slack variables to the three inequalities and obtain x + y + z + s 1 = 15 x + s 2 = 3 2 y − z + s 3 = 0 The objective function can be rewritten as − 531 x − 472 y − 354 z + p = 0 The initial simplex tableau is [ x y z s 1 s 2 s 3 p 1 1 1 1 0 0 0 15 1 0 0 0 1 0 0 3 0 2 − 1 0 0 1 0 0 − 531 − 472 − 354 0 0 0 1 0 ] _ The column corresponding to x has the highest negative value in the row and thus would enter the basis. The pivot element can be found by calculating the ratio of the elements in the extreme right column and the column corresponding to the entering variable. 15 1 = 15 3 1 = 3 The minimum ratio is 3, so s 2 leaves the basis. − R 1 + R 2 → R 2 , 531 R 2 + R 4 → R 4 gives [ x y z s 1 s 2 s 3 p 0 1 1 1 − 1 0 0 12 1 0 0 0 1 0 0 3 0 2 − 1 0 0 1 0 0 0 − 472 − 354 0 531 0 1 1593 ] _ The column corresponding to y has the highest negative value in the row and thus would enter the basis

11th Edition

ISBN: 9780321979438

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

Publisher: PEARSON

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Chapter 4.2, Problem 35E

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The number of hours Lauren should spend on each exercise to maximize the number of calories burnt and the final maximum number of calories burnt.

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Chapter 4.2, Problem 34E

Chapter 4.2, Problem 36E

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Chapter 4 Solutions

Finite Mathematics (11th Edition)

Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 2E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 4E Ch. 4.1 - For Exercises 5-8. (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - Introduce slack variables as necessary, then...Ch. 4.1 - Introduce slack variables as necessary, then write...

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The number of hours Lauren should spend on each exercise to maximize the number of calories burnt and the final maximum number of calories burnt.

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