Question

A farmer has a 100-acre farm on which to plant watermelons and cantaloupes. Every acre with watermelons requires 50 gallons of water per day and must be prepared for planting with 20 pounds of fertilizer. Every acre 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 $3 each and cantaloupes will sell for $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 proposes from a sallow 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 units he produces, how many acres of each crop should the farmer plant in order to maximize profits?

To solve this, you will need to calculate per acre costs for fertilizer and labor and subtract that from the profit.

Put this problem on a sheet named "Farm." Solve this and call the first answer report "Original." Now the farmer believes due to heavy rains, his shallow well could produce 7,000 gallons of water daily. Make this change and solve. Name the answer report "7000 gallons." Now change the number of gallons of water available daily back to 6,000. The labor rate needs to change to $9.00 an hour. Make the change and solve again. Name the answer report, "9,00 labor." In a textbox on the sheet with your calculations, answer the following.

1. According to the original report, how many acres of each type of produce should be planted?

2. Would increasing the water available be profitable to the farmer? Why or why not? Does the product mix change? If so, how?

3. Did the increase in wage rate change the product mix (the number of acres of cantaloupes and watermelons) from the original problem? What impact did the wage increase have?

Answer 1

Original
	watermeln	Cantaloupes		Acres available	100
Water gallons	50	75		water available gallons	6000
Fertilizers pounds	20	15		Fertilizer cost per 50 pound	10
Labour hours	2	2.5		Fertilizer cost per pound	0.2
Sale price	3	1
Per acre units	90	300
Sale price (per acre)	270	300
Labour cost @ 5/hr	10	12.5
Fertilizer cost@ $10/50 pounds	4	3
Profit per acre	256	284.5
Original
Divide 6000 gallons for 100 acres	3000	3000
Acres available	60	40
Profit per acre	256	284.5
Total profit	15360	11380	26740
7000 gallons
Divide 7000 gallons for 100 acres	1000	6000
Acres available	20	80
Profit per acre	256	284.5
Total profit	5120	22760	27880
9,00 Labour
Divide 6000 gallons for 100 acres	3600	1600
Acres available	60	40
Profit per acre	256	284.5
Less additional labour cost	4	4
Revised profit per acre	252	280.5
Total profit	15120	11220	26340

1)	60 acres of watermelon and 40 acres of cantaloupes
2)	Yes, available water to be distributed between both products and cant allocate fully to cantaloupes for higher profit (6000 gallons to 80 acres means 20 acres is left idle. If water available is increased, per acre water availbility increases allowing more acres to cantaloupes
3)	No, rate change doesnt impact product mix as this changes for both products and its per acre cost regardless of which product