A farmer 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 $3.00 each, and cantaloupes will sell for about $1.00 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 in order to maximize profits?

a. Find the optimal solution to maximize profits.

Use Solver Sensitivity Reports and answer the following questions:

b. How much can the price of watermelons drop before it is no longer optimal to plant any watermelons?

c. How much does the price of cantaloupes have to increase before it is optimal to only grow cantaloupes?

d. Suppose the price of watermelons drops by $60.00 per acre and the price of cantaloupes increases by $50.00 per acre. Is the current solution still optimal?

e. Suppose the farmer can lease up to 20 acres of land from a neighboring farm to plant additional crops. How many acres should the farmer lease and what is the maximum amount he should pay to lease each acre?