SOLUTION: A farmer cooperative mixes two brands of cattle feed. Brand x cost $25 per bag and contains 2 units of nutritional element A, 2 units of element B, and 2 units of element C. Brand

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Question 411817: A farmer cooperative mixes two brands of cattle feed. Brand x cost $25 per bag and contains 2 units of nutritional element A, 2 units of element B, and 2 units of element C. Brand Y costs $20 per bag and contains 1 unit of nutritional A, 9 units of B and 3 units of C. Find the number of bags of each brand that should be mixed to provide a mixture having a minimum cost per bag. Requirements of nutrients A: 12 B:36 C:24 units.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Brand x cost $25 per bag and contains 2 units of nutritional element A, 2 units of element B,
and 2 units of element C.
:
Brand Y costs $20 per bag and contains 1 unit of nutritional A, 9 units of B and 3 units of C.
:
Find the number of bags of each brand that should be mixed to provide a mixture having a minimum cost per bag.
:
Requirements of nutrients A: 12 B:36 C:24 units.
:
Let x = no. of bags of x
Let y = no. of bags of y
:
Write an equation for each element, put in the slope/intercept for graphing
element A equation
2x + 1y = 12
y = -2x + 12 (Red)
:
element B equation
2x + 9y = 36
9y = -2x + 36
y = -2%2F9x + 4; (green)
:
element C equation
2x + 3y = 24
3y = -2x + 24
y = -2%2F3 + 8; (purple)
:
Graph these three equations

:
I'm going to say 3 bags of x, and 6 bags of y