Aresearcher wants to provide a rabbit exactly 162 units ofprotein, 72 units of carbohydrates, and 30 units of vitamin a. the rabbit is fed three types of food. each gram of food a has 5 units of protein, 2 units of carbohydrates, and 1unit of vitamin a. each gram of food b contains 11 units of protein, 5 units ofcarbohydrates, and 2 units of vitamin a. each gram of food c contains 23 units of protein, 11 units of carbohydrates, and 4 units of vitamin a. how many grams of each food should the rabbit be fed?

The rabbit should be fed:

grams of food A

grams of food B

grams of food C

For .

Step-by-step explanation:

This can be solved by a system of equations.

I am going to say that x is the number of grams of food A, y is the number of grams of food B and z is the number of grams of Food C.

The problem states that:

A researcher wants to provide a rabbit exactly 162 units of protein:

There are 5 units of protein in each gram of food A, 11 units of protein in each gram of food B and 23 units of protenin in each gram of food C. So

A researcher wants to provide a rabbit exactly 72 units of carbohydrates:

There are 2 units of carbohydrates in each gram of food A, 5 units of carbohydrates in each gram of food B and 11 units of carbohydrates in each gram of food C. So:

A researcher wants to provide a rabbit exactly 30 units of Vitamin A:

There is 1 unit of Vitamin A in each gram of food A, 2 units of Vitamin A in each gram of food B and 4 units of Vitamin A in each gram of food C. So:

.

We have to solve the following system of equations:

.

I think that the easier way to solve this is reducing the augmented matrix of this system.

This system has the following augmented matrix:

To help reduce this matrix, i am going to swap the first line with the third

Now we have the following matrix:

Now i am going to do these following operations, to reduce the first row:

Now we have

Now, to reduce the second row, i do:

The matrix is:

This means that z is a free variable, so we are going to write y and x as functions of z.

From the second line, we have

From the first line, we have

Our solution is: .

However, we can not give a negative number of grams of a food. So

The rabbit should be fed:

grams of food A

grams of food B

grams of food C

For .

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