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 maximize her profit.

Answer 1

Let x be the number of loaves of banana bread and y be the number of loaves of nyt bread Elena makes.

1. A loaf of banana bread requires 2 cups of flour and 2 eggs, then x loaves require 2x cups of flour and 2x eggs.

2. A loaf of nut bread takes 3 cups of flour and 1 egg, then y loaves require 3y cups of flour and y eggs.

3. Elena has 12 cups flour, then

2x+3y≤12.

4. Elena has 8 eggs, then

2x+y≤8.

5. If she makes $1.50 profit per loaf of banana bread and $2 per loaf of nut bread, then she makes total profit of $(1.50x+2y).

The solution of system of two inequalities

$\left\{\begin{array}{l}2x+3y\le 12\\2x+y\le 8\end{array}\right.$

is represented in the attached diagram.

The maximal profit can be obtained at point (3,2), where

$\ (1.50\cdot 3+2\cdot 2)=\ 8.5.$

Answer: correct choice is C (Elena could make 3 loaves of banana bread and 2 loaves of nut bread to maximize her profit)

Answer 2

Let x be the number of loaves of banana bread and y be the number of loaves of nyt bread Elena makes.

1. A loaf of banana bread requires 2 cups of flour and 2 eggs, then x loaves require 2x cups of flour and 2x eggs.

2. A loaf of nut bread takes 3 cups of flour and 1 egg, then y loaves require 3y cups of flour and y eggs.

3. Elena has 12 cups flour, then

2x+3y≤12.

4. Elena has 8 eggs, then

2x+y≤8.

5. If she makes $1.50 profit per loaf of banana bread and $2 per loaf of nut bread, then she makes total profit of $(1.50x+2y).

The solution of system of two inequalities is represented in the attached diagram.The maximal profit can be obtained at point (3,2), where Answer: correct choice is C (Elena could make 3 loaves of banana bread and 2 loaves of nut bread to maximize her profit)