Juiceco manufactures two products: premium orangejuice and regular orange juice. Both products are made bycombining two types of oranges: grade 6 and grade 3. Theoranges in premium juice must have an average grade of atleast 5, those in regular juice, at least 4. During each of thenext two months Juiceco can sell up to 1,000 gallons ofpremium juice and up to 2,000 gallons of regular juice.Premium juice sells for $1.00 per gallon, while regular juicesells for 80¢ per gallon. At the beginning of month 1, Juicecohas 3,000 gallons of grade 6 oranges and 2,000 gallons ofgrade 3 oranges. At the beginning of month 2, Juiceco maypurchase additional grade 3 oranges for 40¢ per gallon andadditional grade 6 oranges for 60¢ per gallon. Juice spoils atthe end of the month, so it makes no sense to make extra juiceduring month 1 in the hopes of using it to meet month 2demand. Oranges left at the end of month 1 may be used toproduce juice for month 2. At the end of month 1 a holdingcost of 5¢ is assessed against each gallon of leftover grade 3oranges, and 10¢ against each gallon of leftover grade 6oranges. In addition to the cost of the oranges, it costs 10¢ toproduce each gallon of (regular or premium) juice. Formulatean LP that could be used to maximize the pro?t (revenues 2costs) earned by Juiceco during the next two months.
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