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 $1.50 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 1,290 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.

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

Let

A = Number of Apple pies to be produced

G = Number of Grape pies to be produced

Max 1.5A + 1.2G

s.t.

1.5A+2G <= 1290

3A+3G <= 1890

A, G >= 0

Solution using LINGO is following:

Optimal solution:

Apple pies = 630

Grape pies = 0

Total profit = 1.5*630+1.2*0 = $ 945

Unused Sugar = 1290 - (1.5*630+2*0) = 345 cups

Unused Flour = 1890 - (3*630+3*0) = 0 cups

Time required for each item as well as available time is not given in the question. Therefore, unused time cannot be computed.