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A weight lifter wants to mix two types of protein powder. One is a whey protein and one is a soy protein. The fat, carbohydrate, and protein content (in grams) for 1 scoop of each powder is given in the table. Fat Carbohydrates Protein Whey 3 g 3 g 20 g Soy 2g 4 g 18 g Suppose that the weight lifter wants to make at most 60 scoops of a protein powder mixture. Furthermore, he wants to limit the total fat content to at most 150 g and the total carbohydrate content to at most 216 g. a. Determine the number of scoops of each type of powder that will maximize the total protein content under these constraints. b. What is the maximum total protein content? c. If the protein content were reversed between the two brands (that is, 18 g for the whey protein and 20 g for the soy protein), then how much of each type of protein powder should be used to maximize the amount of protein?

A weight lifter wants to mix two types of protein powder. One is a whey protein and one is a soy protein. The fat, carbohydrate, and protein content (in grams) for 1 scoop of each powder is given in the table. Fat Carbohydrates Protein Whey 3 g 3 g 20 g Soy 2g 4 g 18 g Suppose that the weight lifter wants to make at most 60 scoops of a protein powder mixture. Furthermore, he wants to limit the total fat content to at most 150 g and the total carbohydrate content to at most 216 g. a. Determine the number of scoops of each type of powder that will maximize the total protein content under these constraints. b. What is the maximum total protein content? c. If the protein content were reversed between the two brands (that is, 18 g for the whey protein and 20 g for the soy protein), then how much of each type of protein powder should be used to maximize the amount of protein?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 11P
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A weight lifter wants to mix two types of protein powder. One is a whey protein and one is a soy protein. The fat, carbohydrate, and protein content (in grams) for 1 scoop of each powder is given in the table. Fat Carbohydrates Protein Whey 3 g 3 g 20 g Soy 2g 4 g 18 g Suppose that the weight lifter wants to make at most 60 scoops of a protein powder mixture. Furthermore, he wants to limit the total fat content to at most 150 g and the total carbohydrate content to at most 216 g. a. Determine the number of scoops of each type of powder that will maximize the total protein content under these constraints. b. What is the maximum total protein content? c. If the protein content were reversed between the two brands (that is, 18 g for the whey protein and 20 g for the soy protein), then how much of each type of protein powder should be used to maximize the amount of protein?
Transcribed Image Text:A weight lifter wants to mix two types of protein powder. One is a whey protein and one is a soy protein. The fat, carbohydrate, and protein content (in grams) for 1 scoop of each powder is given in the table. Fat Carbohydrates Protein Whey 3 g 3 g 20 g Soy 2g 4 g 18 g Suppose that the weight lifter wants to make at most 60 scoops of a protein powder mixture. Furthermore, he wants to limit the total fat content to at most 150 g and the total carbohydrate content to at most 216 g. a. Determine the number of scoops of each type of powder that will maximize the total protein content under these constraints. b. What is the maximum total protein content? c. If the protein content were reversed between the two brands (that is, 18 g for the whey protein and 20 g for the soy protein), then how much of each type of protein powder should be used to maximize the amount of protein?
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