Question

Juiceco manufactures two products: premium orange juice and regular orange juice. Both
products are made by combining two types of oranges: grade 6 and grade 3. The oranges in
premium juice must have an average grade of at least 5, those in regular juice, at least 4.
During each of the next two months Juiceco can sell up to 1,000 gallons of premium juice and
up to 2,000 gallons of regular juice. Premium juice sells for $1,00 per gallon while regular
juice sells for 80 cents per gallon. At the beginning of month 1 Juiceco has 3,000 gallons of
grade 6 oranges and 2,000 gallons of grade 3 oranges. At the beginning of month 2, Juiceco
may purchase additional grade 3 oranges for 40 cents per gallon and additional grade 6
oranges for 60 cents per gallon. Juice spoils at the end of the month, so it makes no sense to
make extra juice during month 1 in the hopes of using it to meet month 2 demand. Oranges
left at the end of month 1 may be used to produce juice for month 2. At the end of month 1 a
holding cost of 5 cents is assessed against each gallon of leftover grade 3 oranges and 10 cents
against each gallon of leftover grade 6 oranges. In addition to the cost of the oranges it costs
10 cents to produce each gallon of (regular or premium) juice. Formulate an LP that could be
used to maximize the profit (revenues-costs) earned by Juiceco during the next two months.

Please formulate the LP problem and not provide coding.

Answer 1