A retired couple supplement their income by making fruit pies, which they sell to a local...
A retired couple supplement their income by making fruit pies,
which they sell to a local grocery store. During the month of
September, they produce apple and grape pies. The apple pies are
sold for $1.40 to the grocer, and the grape pies are sold for
$1.25. The couple is able to sell all of the pies they produce
owing to their high quality. They use fresh ingredients. Flour and
sugar are purchased once each month. For the month of September,
they have 1,150 cups of sugar and 1,800 cups of flour. Each apple
pie requires 1½ cups of sugar and 3 cups of flour, and each grape
pie requires 2 cups of sugar and 3 cups of flour.
a. Determine the number of grape and the number of
apple pies that will maximize revenues if the couple working
together can make an apple pie in 8 minutes and a grape pie in 2
minutes. Together, they plan to work no more than 45 hours.
(Round your answers to nearest whole number. Omit the "$"
sign in your response.)
| Apple | ____ | Pieces |
| Grape | _____ | Pieces |
| Revenue | $____ | |
b. Determine the amounts of sugar, flour, and time
that will be unused. (Leave no cells blank - be certain to
enter "0" wherever required. Round your intermediate calculations
and final answers to the nearest whole number.)
| Sugar____ | cups | |
| Flour_____ | cups | |
| Time_____ | minutes | |
Homework Answers
Here, let me consider Number of Apple Pies=X1
Number of Grape Pies=X2
They want to Maximize the sales Revenue, hence, Maximize Objective function=1.40*X1+1.25*X2
Constraints:
Sugar: 1.5*X1+2*X2=<1150
Flour: 3*X1+3*X2=<1800
8*X1+2*X2=<2700
X1 and X2>=0
Here, I will use graphical method to calculate the value of X1 and X2
Number of Apple Pies=250 pieces
Number of Grape Pies=350 pieces
Maximize the sales Revenue =1575/2=$787.5
Sugar=1.5*X1+2*X2=(1.5*250)+(2*350)=1075 cups
Flour=3*X1+3*X2=(3*250)+(3*350)=1800 Cups
Time=8*X1+2*X2=(8*250)+(2*350)=2700 Minutes
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A retired couple supplement their income by making fruit pies,
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