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, must have an average grade of at least 4. During each of the next two months, Juiceco can sell up to 1000 gallons of premium juice and up to 2000 gallons of regular juice. Premium juice sells for $1 per gallon and regular juice sells for $.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 $.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 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 the month a holding cost of $.05 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 oranges, it cost $.10 to produce each gallon of (regular or premium) juice. Use linear programming to determine the mixture of oranges that maximizes profit (revenue - cost)

Answer 1