Question

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 $1.55 to the grocer, and the grape pies are sold for $1.20. 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 1,240 cups of sugar and 1,890 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 7 minutes and a grape pie in 4 minutes. Together, they plan to work no more than 55 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

Answer 1

LP Model:

a)
fruit pies	price	flour	sugar	time (min)
apple pies	$1.55	3	1.5	7
grape pies	$1.20	3	2	4
max. availability		1890	1240	3300
Decision variables: Let a,g be the number of pies made in September
objective function:
maximize revenue
revenue = 1.55a+1.20g
constraints:
a,g>=0,int	non-negativity
3a+3g<=1890	flour availability
1.5a+2g<=1240	sugar availability
7a+4g<=3300	time availability

model in Excel:

solver solution:

a)
Apple	260	Pieces
Grape	370	Pieces
Revenue	847
b)
Sugar	110	cups
Flour	0	cups
Time	0	minutes