A diet supplies 0.8 grams of calcium per day, in addition to the nutrients listed in the table to the right. The amounts of calcium per unit (100 g) supplied by the three ingredients in the diet are as follows: 1.25 g from nonfat milk, 0.18 g from soy flour, and 0.8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 78 g of protein, 0 g of carbohydrate, 3.6 g of fat, and 0.15 g of calcium. Complete parts (a) and (b) below. Amounts (g) Supplied per 100 Amounts (g) g of Ingredient Nutrient Supplied by Nonfat Soy Whey Diet in One Milk flour Day 36 Protein Carbohydrate 52 0 Fat 50 33 7 4 75 12 14 34 45 3 a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy proteimm necessary to supply the precise amounts of protein, carbohydrate, fat, and calcium in the diet.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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A diet supplies 0.8 grams of calcium per day, in addition to
the nutrients listed in the table to the right. The amounts of
calcium per unit (100 g) supplied by the three ingredients in
the diet are as follows: 1.25 g from nonfat milk, 0.18 g from
soy flour, and 0.8 g from whey. Another ingredient in the diet
mixture is isolated soy protein, which provides the following
nutrients in each unit: 78 g of protein, 0 g of
carbohydrate, 3.6 g of fat, and 0.15 g of calcium. Complete
parts (a) and (b) below.
0.42
X₁
x2
X3
11
34
45
3
0.8
CIES
X4
(Type an integer or decimal for each matrix element.)
Amounts (g) Supplied per 100 Amounts (g)
g of Ingredient
Supplied by
Diet in One
Day
a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein
necessary to supply precise amounts of protein, carbohydrate, fat, and calcium in the diet.
Nutrient Nonfat Soy Whey
Milk flour
36
Protein
Carbohydrate 52
0
Fat
50 14
33
75
7
1.2
34
45
3
Transcribed Image Text:A diet supplies 0.8 grams of calcium per day, in addition to the nutrients listed in the table to the right. The amounts of calcium per unit (100 g) supplied by the three ingredients in the diet are as follows: 1.25 g from nonfat milk, 0.18 g from soy flour, and 0.8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 78 g of protein, 0 g of carbohydrate, 3.6 g of fat, and 0.15 g of calcium. Complete parts (a) and (b) below. 0.42 X₁ x2 X3 11 34 45 3 0.8 CIES X4 (Type an integer or decimal for each matrix element.) Amounts (g) Supplied per 100 Amounts (g) g of Ingredient Supplied by Diet in One Day a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply precise amounts of protein, carbohydrate, fat, and calcium in the diet. Nutrient Nonfat Soy Whey Milk flour 36 Protein Carbohydrate 52 0 Fat 50 14 33 75 7 1.2 34 45 3
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