# Formulate and then solve a linear programming model

August 30, 2017

Question
A company makes four juice product using orange, grapefruit and pineapple juice.

Product Retail Price per Quart
Orange Juice \$1.00
Grapefruit Juice \$0.90
Pineapple Juice \$0.80
All-in-one Juice \$1.10

The all-in-one juice has equal parts of orange, grapefruit and pineapple juice. Each product is produced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of orange juice, 300 gallons of grapefruit juice and 200 gallons of pineapple juice. The cost per gallon is \$2.00 for orange juice, \$1.60 for grapefruit juice and \$1.40 for Pineapple juice.
In addition, the manager wants grapefruit juice to be used for no more than 30 percent of the number of containers produced. She wants the ratio of the number of containers of orange juice to the number of containers of pineapple juice to be at least 7 to 5?

A. Formulate a linear programming model to determine how many containers of each product to produce tomorrow to maximize profits.

B. Solve the model Using Excel Solver.

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