Question

Kari is making baked goods for a party. Each batch of cookies use 2 eggs and 4 cups of flower. Each batch of cupcakes use 4 eggs and 3 cups of flower. Kari has 2 dozen eggs and 30 cups of flower on hand. How many batches of each should Kari make to maximize the amount of servings? If a single batch of cookies and cupcakes makes 12 servings, how many servings will she have if she maximizes her amount?

Answer 1

A. 4 batches of Cookies

4 batches of Cupcakes.

B. 48 servings.

Explanation:

A.

To make a batch of:

Cookies:

2 eggs

4 cups of flower

Cupcakes:

4 eggs

3 cups of flower

Kari has 2 dozen of eggs (2*12) and 30 cups of flour.

Let the eggs and cups of flour be denoted as X and Y respectively.

Cookies: 2X + 4Y

Cupcakes: 4X + 3Y

Since Kari has 24 X and 30 Y, (Expressed as whole numbers).

2X + 4X = 24,

X = 4

4Y + 3Y = 30

Y = 4

Therefore, the maximum amount of batches is:

4 batches of Cookies

4 batches of Cupcakes.

B.

Since, 1 batch of Cookies + 1 batch of Cupcakes = 12 servings

Therefore, 4 batch of Cookies + 4 batch of Cupcakes = (12*4) servings

= 48 servings.