A farmer in Georgia has a 200-acre farm on which to plant watermelons and cantaloupes. Every acre planted with watermelons requires 50 gallons of water per day. Each acre planted with watermelons must also be prepared for planting with 20 pounds of fertilizer. Every acre planted with cantaloupes requires 75 gallons of water per day. Each acre planted with cantaloupes must also 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 14,000 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 $13 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? (Let X, be the number of watermelons the farm should plant and let X, be the number of cantaloupes the farm should plant.) Implement a spreadsheet model for this problem and solve it using Solver. How many acres of each crop should the farmer plant in order to maximize profits? What is the maximum profit (in dollars)? Need Help? Read It
A farmer in Georgia has a 200-acre farm on which to plant watermelons and cantaloupes. Every acre planted with watermelons requires 50 gallons of water per day. Each acre planted with watermelons must also be prepared for planting with 20 pounds of fertilizer. Every acre planted with cantaloupes requires 75 gallons of water per day. Each acre planted with cantaloupes must also 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 14,000 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 $13 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? (Let X, be the number of watermelons the farm should plant and let X, be the number of cantaloupes the farm should plant.) Implement a spreadsheet model for this problem and solve it using Solver. How many acres of each crop should the farmer plant in order to maximize profits? What is the maximum profit (in dollars)? Need Help? Read It
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A farmer in Georgia has a 200-acre farm on which to plant watermelons and cantaloupes. Every acre planted with watermelons requires 50 gallons of water per day. Each acre planted with watermelons must also be prepared for planting with 20 pounds of fertilizer. Every
acre planted with cantaloupes requires 75 gallons of water per day. Each acre planted with cantaloupes must also 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 14,000 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 $13 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? (Let X, be the number of watermelons the farm should plant and let
X, be the number of cantaloupes the farm should plant.)
Implement a spreadsheet model for this problem and solve it using Solver.
How many acres of each crop should the farmer plant in order to maximize profits?
(X1, X2) =
What is the maximum profit (in dollars)?
$
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