An animal breeder can buy four types of food for Vietnamese​ pot-bellied pigs. Each case of Brand A contains 25 units of​ fiber, 40 units of​ protein, and 40 units of fat. Each case of Brand B contains 50 units of​ fiber, 40 units of​ protein, and 40 units of fat. Each case of Brand C contains 125 units of​

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.1: Solution Of Linear Systems
Problem 46E
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An animal breeder can buy four types of food for Vietnamese​ pot-bellied pigs. Each case of Brand A contains
25
units of​ fiber,
40
units of​ protein, and
40
units of fat. Each case of Brand B contains
50
units of​ fiber,
40
units of​ protein, and
40
units of fat. Each case of Brand C contains
125
units of​ fiber,
80
units of​ protein, and
100
units of fat. Each case of Brand D contains
50
units of​ fiber,
40
units of​ protein, and
20
units of fat. How many cases of each brand should the breeder mix together to obtain a food that provides
1725
units of​ fiber,
1200
units of​ protein, and
1380
units of​ fat?
 
 
 

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Part 1 of 4 (refer to problem for next steps)
Let x represent the number of cases of Brand​ A, y represent the number of cases of Brand​ B, z represent the number of cases of Brand​ C, and w represent be the number of cases of Brand D. There are four ways in which the breeder can mix brands to obtain a food that provides
1725
units of​ fiber,
1200
units of​ protein, and
1380
units of fat.
 
If
w=​0,
the solution is
​(enter your response here​,
enter your response here​,
enter your response here​,
​0).
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Following up on this questiona nd its process, what would the solution be if w=1? w=2? These matrices and Gauss-Jordan problems are my everest. Thank you so much!

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