Question
Each week, Florida Citrus, Inc., uses a single machine for 150 hours to distill orange and grapefruit juice into concentrates that are then stored in
Each week, Florida Citrus, Inc., uses a single machine for 150 hours to distill orange and grapefruit juice into concentrates that are then stored in two separate 1000-gallon tanks (one for orange juice and one for grapefruit juice) before being frozen. The machine can process 25 gallons of orange juice per hour but only 20 gallons of grapefruit juice. Each gallon of orange juice cost $1.50 and loses 30% in water content when distilled into a concentrate that then sells for $6.00 per gallon. Each gallon of grapefruit juice costs $2.00 and loses 25% when distilled into a concentrate that then sells for $8.00 per gallon. Formulate a model to determine a production plan to maximize the profit for the coming week using the following variables: OJ = the number of gallons of orange juice to use this week, GJ = the number of gallons of grapefruit juice to use this week.
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