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jarptica [38.1K]
3 years ago
8

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.

Mathematics
2 answers:
9966 [12]3 years ago
6 0

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)

ehidna [41]3 years ago
5 0

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)

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Answer:

Step-by-step explanation:


So in this example we'll be using the difference of squares which essentially states that: (a-b)(a+b)=a^2-b^2 or another way to think of it would be: a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}). So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

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Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

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So completely factored form is: (x^2-2)(x^2+4)(x^4+4)

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7 0
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