Matrix..

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• Nov 19th 2006, 07:44 PM
eureka
Matrix..
Hi There;

A rancher has to mix three types of feed for her cattle. The following analysis shows the amounts per bag of grain:

Grain Protein (kg) Carbohydrates (kg) Sodium (kg)
A 7 88 1
B 6 90 1
C 10 70 2

How many bags of each type of grain should she mix to provide 71kg of protein, 854 kg of carbohydrates and 12kg of sodium?
• Nov 19th 2006, 08:35 PM
CaptainBlack
Quote:

Originally Posted by eureka
Hi There;

A rancher has to mix three types of feed for her cattle. The following analysis shows the amounts per bag of grain:

Grain Protein (kg) Carbohydrates (kg) Sodium (kg)
A 7 88 1
B 6 90 1
C 10 70 2

How many bags of each type of grain should she mix to provide 71kg of protein, 854 kg of carbohydrates and 12kg of sodium?

Let a, b and c denote the number of bags of each grain required then
we have:

7a + 6b + 10c = 71 ..protien equation

88a + 90b + 70c = 854 ..carb. equation

a + b + 2c = 12 ..sodium equation.

These constitute a set of simultaneous linear equations which you should
solve.

RonL
• Nov 20th 2006, 08:08 AM
Soroban
Hello, eureka!

Quote:

A rancher has to mix three types of feed for her cattle.
The following analysis shows the amounts per bag of grain:

$\displaystyle \begin{array}{ccccc} \text{Grain} & \text{Protein} & \text{Carb.} & \text{Sodium}\\ \hline \\ A & 7 & 88 & 1 & \\ B & 6 & 90 & 1 \\ C & 10 & 70 & 2\\ \hline \\ \text{Req.} & 71 & 854 & 12 \end{array}$

How many bags of each type of grain should she mix to provide
the requirements for protein, carbohydrates, and sodium?

Captain Black is absolutely correct.

The system of equation is: .$\displaystyle \begin{array}{ccc}7a + 6b + 10c \\ 88a + 40b + 70c \\ a + b + 2c\end{array} \begin{array}{ccc}= \\ = \\ = \end{array} \begin{array}{ccc}72 \\ 854 \\ 12\end{array}$

You said "matrix", so this is your quest . . .

Solve: . $\displaystyle \begin{pmatrix}7 & 6 & 10 & | & 71 \\ 88 & 40 & 70 & | & 854 \\ 1 & 1 & 2 & | & 12\end{pmatrix}$