Formulate and then solve a linear programming model of this problem, to determine how many containers of each product to produce tomorrow to maximize profits. The company makes four juice products using orange, grapefruit, and pineapple juice.

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, $1.6 for grapefruit juice, and $1.40 for pineapple juice. In addition, the manager wants grapefruit juice containers to be 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. NOTE: You will need to use Excel Solver to be able to answer these questions.

a. Which of the following are constraints in this problem?

1. On hand are 400 gallons of orange juice, 300 gallons of grapefruit juice, and 200

gallons of pineapple juice.

i. The cost per gallon is $2.00 for orange juice, $1.6 for grapefruit juice, and $1.40 for

pineapple juice.

ii.In addition, the manager wants grapefruit juice containers to be no more than 30

percent of the number of containers produced.

iii.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.

b. Use Excel Solver to obtain the optimal solution.