Question

1. A retired couple supplement their income by making fruit pies, which the sell to a nearby grocery store. The grape pies are sold for $1.50 and the apple pies for $1.20. The couple believes that they can sellall the grape pies they produce but no more than 150 apple pies. They use fresh ingredients. Flour and sugar are purchased once a month. For the month of September, they have 1,300 cups of sugar and 2,200 cups of flour. Each apple pie requires one and a half cups of sugar and three cups of flour, and each grape pie requires two cups of sugar and three cups of flour. The couple working together can make an apple pie is six minutes and a grape pie in three minutes. The plan to work no more than 60 hours Formulate as a Linear Programming problem (Do not solve)
Plz show work if Possible

Answer 1

Linear program is following:

Let G and A be the number of Grape and Apple pies resp that the couple should make in the month of September

Maximize 1.5G + 1.2A

s.t.

A <= 150

2G + 1.5A <= 1300   (cups of sugar)

3G + 3A <= 2200   (cups of flour)

3G + 6A <= 3600 (60 hours = 3600 minutes)

G, A >= 0