Question

Elena makes banana bread and nut bread to sell at the market. A loaf of banana bread requires 2 cups of flour and 2 eggs. A loaf of nut bread takes 3 cups of flour and 1 egg. Elena has 12 cups flour and 8 eggs on hand. If she makes $1.50 profit per loaf of banana bread and $2 per loaf of nut bread, how many loaves of banana bread and nut bread could she make that will maximize her profit? A. Elena could make 0 loaves of banana bread and 4 loaves of nut bread to maximize her profit. B. Elena could make 2 loaves of banana bread and 3 loaves of nut bread to maximize her profit. C. Elena could make 3 loaves of banana bread and 2 loaves of nut bread to maximize her profit. D. Elena could make 1 loaf of banana bread and 5 loaves of nut bread to maxim

Answer 1

The answer is Elena could make 3 loaves of banana bread and 2 loaves of nut bread to maximize her profit

Answer 2

The correct answer is option C

Explanation:

Let the number of loaves of banana bread be = x

Let the number of loaves of nut bread be = y

As given, a loaf of banana bread requires 2 cups of flour and 2 eggs, then x loaves will need 2x cups of flour and 2x eggs. Similarly, a loaf of nut bread needs 3 cups of flour and 1 egg, then y loaves will need 3y cups of flour and y eggs.

Also give is , Elena has 12 cups flour and 8 eggs then equations with respect to flour and eggs become :

2x+3y≤12 (flour)

2x+y≤8 (eggs)

Its stated that if Elena makes $1.50 profit per loaf of banana bread and $2 per loaf of nut bread, so she makes a total profit of 1.50x+2y .... (a)

Now, to solve the maximum profit we will make a graph. Please find attached the graph. The maximum profit is calculated at point (3,2)

Now putting x as 3 and y as 2 in equation (a)

1.50*3+2*2 = 4.5+4 = $8.5

Hence, Elena could make 3 loaves of banana bread and 2 loaves of nut bread to maximize her profit.