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 $1.60 to the grocer, and the grape pies are sold for $1.30. 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 1,200 cups of sugar and 1,850 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 5 minutes and a grape pie in 3 minutes. Together, they plan to work no more than 50 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

(a)

Let the number of apple pies made be a and number of grape pie made be g

Objective -

Max Revenue Z = 1.6a + 1.3g

Constraints

5a + 3g <= 3000 .... Time constraint

1.5a + 2g <= 1200 .... Sugar constraint

3a + 3g <= 1850 .... flour constraint

Let us solve using excel solver -

We need to find out the values in green cell (number of apple and grape pies) to maximize the revenue. the constraints are applied in the blue cells.

Solve to get -

Hence,

Number of Apple Pies made - 576

Number of Grape Pies made - 40

Total Revenue - $973.6

(b)

Amount of unused sugar = 1200 - 944 = 256

Amount of unused flour = 1850 - 1848 = 2

Amount of time unused = 3000 - 3000 = 0 mins