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. Assume that the grade of a mixture of the two oranges can be determined by averaging the grades. For example, one gallon of grade 6 oranges mixed with two gallons of grade 3 oranges would result in three gallons of grade 4 juice. The oranges in premium juice must have an average grade of at least 5, those in regular juice, at least 4.
During month 1 Juiceco can sell up to 1000 gallons of premium juice and up to 2000 gallons of regular juice. During month 2 Juiceco can sell up to 1000 gallons of premium juice and up to 2000 gallons of regular juice. Premium juice sells for $1.00 per gallon, while regular juice sells for $0.80 per gallon.
At the beginning of month 1 Juiceco has 3000 gallons of grade 6 oranges and 2000 gallons of grade 3 oranges. At the beginning of month 2 Juiceco may purchase additional grade 3 oranges for $0.40 per gallon and additional grade 6 oranges for $0.60 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. However, 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 $0.05 is assessed against each gallon of leftover grade 3 oranges, and $0.10 against each gallon of leftover grade 6 oranges. In addition to the cost of the oranges, it costs $0.10 to produce each gallon of (regular or premium) juice.