Problem 1E

The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.

a. Set up a vector equation for this problem. Include a statement of what the variables in your equation represent.

b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared.

Solution:

Step 1 of 1

a.

Let the number of servings of General Mills Cheerios be

Let the number of servings of Quaker 100% Natural Cereals be .

Now,

b. We have .

The equivalent matrix equation for this will be :

To solve we reduce the augmented matrix for this equation, we get

Performing the row operation , we get

Performing the row operation , we get

Performing the row operation , we get

Interchanging row , we get

Performing the row operation , we get

Performing the row operation , we get

Multiplying row by a constant ,we get

Performing the row operation , we get

Performing the row operation , we get

This gives us and .

Yes, the desired mixture can be prepared by taking servings of General Mills Cheerios and 1 serving of Quaker 100% Natural Cereals.