Question 1154674: Brianna makes banana bread and nut bread to sell at a bazaar. A loaf of banana bread requires 2 cup of flour and 2 eggs. A loaf of nut bread takes 3 cups of flour and 1 egg. Brianna has 12 cups of flours and 8 eggs on hand. She makes a $2 profit per loaf of banana bread and $2 per loaf of nut bread. To maximize profits, how many loaves of each type should she bake?
Answer by ikleyn(52751)   (Show Source):
You can put this solution on YOUR website! .
From the profit point of view, the banana bred is equivalent to (is the same as) the nut bread (two dollars each).
Hence, the only trouble is to spend all resources in full.
The difference floor minus eggs is 12 cups of floor minus 8 eggs = 12 - 8 = 4 (different) items.
So, the first step is to make so many loafs of one and the other bread to get the difference 4 between cups and eggs.
It is easy to make MENTALLY: 2 nut breads consume 6 cups and 2 eggs.
The rest 12-6 = 6 cups and 8-2 = 6 eggs she will spend for 3 banana bread loafs.
ANSWER. 2 nut bread loafs and 3 banana bread loafs.
Solved.
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And one after-solution note as a conclusion.
Actually, it is not optimization problem.
it is the problem "to spend all resources in full".
Therefore, as alternative to my MENTAL solution, you may write the system of 2 equations in 2 unknown,
and then solve it.
Instead of doing it, I solved the problem MENTALLY.
This form of solution is good for 7-8-9 years children (who do not know system of equations yet) to exercise their mind.
It is also good as an entertainment problem for people over 70, who just forgot all theirs school Math . . .
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