# math

posted by on .

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 before being frozen. (One tank is for orange juice concentrates and the other is for grape juice concentrates. Two concentrates cannot be mixed.) 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. Find the optimal production plan (the highest profit).

Do this graphically. Plot on the horizontal axis gallons of gfruit juice, and on the vertical axis, orange juice.

Your first point on the graph is (150*20,0), the second (0,150*25).

Then plot constraints: Lines for the tank constaints. Horizontal line at y=1000, and a vertical line at x=1000.

Evaluate the corners for max profit.

I can see something wrong in the construction of this problem: To fill the orange tank, it takes 40 hours, and then to fill the gfruit tank, 50 hours. The machine can't be used for the 150 hours of production, the tanks are a severe limit on profits.

Be certain in the profit function to allow for the shrinkage of the product.