("Farmer in Georgia")A farmer in Georgia has a 100-acre farm where they will plant two crops: watermelons and cantaloupes. Every acre of watermelons planted requires 50 gallons of water per day and must be prepared with 20 pounds of fertilizer.Every acre planted with cantaloupes requires 75 gallons of water per day and must prepared 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.

The farmer believes that watermelons and cantaloupes will sell for about $3 and $1 per unit, respectively. Every acre planted with watermelons is expected to yield 90 salable units, for cantaloupes, even acre planted is expected to yield 300 salable units.

The famer can pump about 6000 gallons of water per day for irrigation purposes from the well. She can buy as much fertilizer as she 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 can sell all the watermelons and cantaloupes that she produces, how many acres of each crop should the farmer plant to maximize profits?

1. Define the decision variables clearly in a sentence.Write (or type) the mathematical formulation for the farmer's problem.
2. Sketch the feasible region on paper by hand either on paper or manually via a technology. Identify and list on the paper each of the feasible corner points. Identify the optimal solution and optimal solution value.
3. Draw at least three "level" curves on the graph create from the part above. Indicate, the direction of improvement. Indicate the optimal solution. Hint:Make the picture big enough.Graph paper is helpful if doing this problem by hand.
4. Enter the data for the problem into Excel and demonstrate the optimal solution matches that from the graphical solution.
5. From the sensitivity report obtained from the optimal solution in part d, answer the following questions with reasoning:
   1. How much can the price of watermelons drop before it is not profitable to grow them?
   2. How much does the price of cantaloupes have to increase to make it profitable to only grow cantaloupes?
   3. Suppose the price of watermelons drops by $60 an acre and the price of cantaloupes increases by $50 an acre. Is the current solution still optimal?
   4. Suppose the farmer can lease up to 20 acres of land from a neighboring farm to plant additional amounts of these two crops. How much should the farmer lease and what is the maximum amount per acre to pay?

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Farmer in Georgia Watermelons Cantalopes Available Water 50 75 6000 gallons/day Acres 100 acres Units per Acre 90 300 units/acre Labor 2 2.5 hours/acre Selling Price per Unit $3.00 $1.00 dollars per unit Fertilizer 20 15 pounds Fetilizer Cost $10.00 per/50 pound bag Labor Cost $5.00 per/hour