A farmer in Georgia has a 100-acre

A farmer in Georgia has a 100-acre farm of 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 hours. If the farmer sells all the watermelons and
cantaloupes he produces, how many acres of each crop should the farmer plant in order to
maximize profits. Formulate and LP model for this problem.P and solve for the optimal solutions that will maximize the
firm’s profit