premium juice

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.


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