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¢ 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¢ per gallon and
additional grade 6 oranges for 60¢ 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¢ is assessed against each gallon of leftover grade 3
oranges, and 10¢ against each gallon of leftover grade 6
oranges. In addition to the cost of the oranges, it costs 10¢ to
produce each gallon of (regular or premium) juice. Formulate
an LP that could be used to maximize the pro?t (revenues 2
costs) earned by Juiceco during the next two months.