Question

A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of June, they produce blueberry and peach pies. The blueberry pies are sold to the grocer for $10.00 and the peach pies are sold for $9.00. The couple is able to sell all of the pies owing to their high quality. They use fresh ingredients. Sugar and flour are bought once a month. The price of sugar per pound is $1.40 and there are roughly 2 cups of sugar in one pound. The price of flour per pound is $0.36 and there are roughly 3.6 cups of flour in one pound. The cost of the fruit needed per pie is the same.

Each blueberry pie requires 1.5 cups of sugar and 3 cups of flour; each peach pie requires 2 cups of sugar and 2.5 cups of flour. On hand are 4 pounds of flour left from the previous month that must be used. There is no shortage of flour, sugar or fruit in the market for them to purchase. The ratio of blueberry pies to peach pies should be at most 4 to 9. The couple working together can make a blueberry pie in 10 minutes and a peach pie in 8 minutes. They plan to work no more than 60 hours during the month of June and do not plan on hiring additional help. Determine the number of blueberry pies and peach pies that will maximize their profit.

Let B = Number of blueberry pies to be baked

Let P = Number of peach pies to be baked

Which of the following is the objective function?

Select one:

a. Max 8.65B + 7.35P

b. Min 1.4S + 0.36F

c. Max 6.82B + 5.3P

d. Max 10B + 9P

e. Min 1.91B + 0.16P

Answer 1

Selling price of blueberry pies = $ 10.00

Price of sugar = $ 1.4 per pound (2 cups)

Price of flour = $ 0.36 per pound (3.6 cups)

Cost of sugar and flour for each blueberry pie = 1.5*1.4/2+3*0.36/3.6

= $ 1.35

Profit for blueberry pie = Selling price - cost of sugar and flour = 10.00 - 1.35

= $ 8.65 per unit

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Selling price of peach pies = $ 9.00

Cost of sugar and flour for each blueberry pie = 2*1.4/2+2.5*0.36/3.6

= $ 1.65

Profit for blueberry pie = Selling price - cost of sugar and flour = 9.00 - 1.65

= $ 7.35 per unit

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Objective of the problem is profit maximization.

Total Profit = Number of blueberry pies to be produced * profit per blueberry pie + Number of peach pies to be produced * profit per peach pie

= 8.65B + 7.35P

Therefore, objective function is: Max 8.65B+7.35P

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ANSWER: a. Max 8.65B + 7.35P