Question 1193938: Jaime runs a bakery that sells two kinds of cookies. Jaime knows the bakery must make at least 29 and at most 45 boxes of the Chocolate Decadence. The bakery must also make between 6 and 26 boxes of the Nutty Squirrels. The boxes of Chocolate Decadence take 13 ounces of sugar, while boxes of Nutty Squirrels require 9 ounces of sugar. The bakery only has 702 ounces of sugar available. If boxes of Chocolate Decadence generate $2.39 in income, and boxes of Nutty Squirrels generate $1.02, how many boxes of the cookies should Jaime have the bakery make to get the most income?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
An informal solution -- since your question has been sitting here for nearly two weeks without a response....
One box of Chocolate Decadence requires 13 ounces of sugar; one box of Nutty Squirrels requires 9 ounces. The amount of sugar available is 702 ounces.
Given one combination of boxes that uses the entire 702 ounces of sugar, another solution can be found by increasing the number of Chocolate Decadence boxes by 9 and decreasing the number of Nutty Squirrel boxes by 13, or vice versa.
Increasing the number of boxes of Chocolate Decadence by 9 increases income by 9($2.39) = $21.51; decreasing the number of boxes of Nutty Squirrels by 13 reduces income by 13(1.02)=$13.26; the net change is an increase of $8.25 in income.
So clearly the bakery should produce the maximum number of boxes of Chocolate Decadence.
The maximum number of boxes of chocolate Decadence is 45, requiring 45*13 = 585 ounces of sugar, leaving 702-585 = 117 ounces of sugar for making Nutty
Squirrels. Since each box of Nutty squirrels requires 9 ounces of sugar, the number of boxes of Nutty Squirrels is 117/9 = 13.
ANSWER: Maximum income is with 45 boxes of Chocolate Decadence and 13 boxes of Nutty Squirrels.
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