# A farmer in Georgia has a 100-acre farm on which

A farmer in Georgia has a 100-acre farm on which to plant watermelons and cantaloupes. Every acre planted with watermelons requires 50 gallons of water per day and must be prepared for planting with 20 pounds of fertilizer. Every acre planted with cantaloupes requires 75 gallons of water per day and must be prepared for planting with 15 pounds of fertilizer. The farmer estimates that it will take 2 hours of labor to harvest each acre planted with watermelons and 2.5 hours to harvest each acre planted with cantaloupes. He believes that watermelons will sell for about \$3 each, and cantaloupes will sell for about \$1 each. Every acre planted with watermelons is expected to yield 90 salable units. Every acre planted with cantaloupes is expected to yield 300 salable units. The farmer can pump about 6,000 gallons of water per day for irrigation purposes from a shallow well. He can buy as much fertilizer as he needs at a cost of \$10 per 50-pound bag. Finally, the farmer can hire laborers to harvest the fields at a rate of \$5 per hour. If the farmer sells all the watermelons and cantaloupes he produces, how many acres of each crop should the farmer plant to maximize profits?

a. Formulate an LP model for this problem.

b. Sketch the feasible region for this model.

c. Find the optimal solution to the problem using level curves.

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