Question

Please answer the question. I have posted this question 3 times......

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,

x1 = number of apple pies to be produced
x2 = number of grape pies to be produced

Objective is to maximize revenue = max 1.6x1+1.3x2

subject to,

1.5x1+2x2 <= 1200 (Sugar)
3x1+3x2 <= 1850 (Flour)
5x1+3x2 <= 3000 (labor hours)

x1,x2 >= 0 (non-negativity constarint)

Solving in solver we get,

Apple = 575 pieces

Grape = 41.66666667 = 42 pieces (rounded to nearest whole number)

Revenue $974.1666667 = $974 (rounded to nearest whole number)

b)

Sugar =1200-946 = 254 cups

Flour = 0 cups

Time = 0 minutes

Solver screenshot

Solver formula