Question

In: Advanced Math

A farmer has 150 acres of land suitable for cultivating Crops A and B. The cost...

A farmer has 150 acres of land suitable for cultivating Crops A and B. The cost of cultivating Crop A is $40/acre, and the cost of cultivating Crop B is $60/acre. The farmer has a maximum of $7400 available for land cultivation. Each acre of Crop A requires 20 labor-hours, and each acre of Crop B requires 25 labor-hours. The farmer has a maximum of 3300 labor-hours available. He has also decided that he will cultivate at least 80 acres of Crop A. If he expects to make a profit of $180/acre on Crop A and $200/acre on Crop B, how many acres of each crop should he plant to maximize his profit?

Crop A     acres
Crop B     acres



What is the maximum profit?
$

Solutions

Expert Solution


Related Solutions

A farmer has 360 acres of land on which to plant corn and wheat. She has...
A farmer has 360 acres of land on which to plant corn and wheat. She has $24,000 in resources to use for planting and tending the fields and storage facility sufficient to hold 18,000 bushels of the grain (in any combination). From past experience, she knows that it costs $120 / acre to grow corn and $60 / acre to grow wheat; also, the yield for the grain is 100 bushels / acre for corn and 40 bushels / acre...
Maximization applications A farmer has 100 acres of land on which she plans to grow wheat...
Maximization applications A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres...
A rancher owns 500 acres of land which is suitable for growing sorghum, corn, and wheat....
A rancher owns 500 acres of land which is suitable for growing sorghum, corn, and wheat. She expects net profits per acre from each crop to be: $55 for sorghum, $60 for corn, and $50 for wheat. She is able to supply 3,000 hours per year of on-farm labor. Additionally, she has 4,500 hours of tractor time available for the production of these three crops. The requirements of each crop are summarized below. Sorghum Corn Wheat Land (acres) 1.0 1.0...
Farmer Brian has 3 acres of land which he farms efficiently. Each acre can support 10...
Farmer Brian has 3 acres of land which he farms efficiently. Each acre can support 10 apple trees. However the 3 acres differ in their ability to support orange trees. He can grow 60 orange trees on the best land, 40 orange trees on the ok land, and 20 orange trees on the bad land. If he initially is using 2 acres to grow apples, what would be the opportunity cost of growing another orange tree? At first I assumed...
A farmer must decide what crops to grow on a 300-hectare tract of land. He can...
A farmer must decide what crops to grow on a 300-hectare tract of land. He can grow oats, wheat, or barley, which yield 50, 100 and 80 kg/hectare (respectively) and sell for $1.00, $0.80, and $0.60 per kg (respectively). Production costs (fertilizer, labor, etc.) are $40, $50, and $40 per hectare for growing oats, wheat and barley, respectively. Government regulations restrict the farmer to a maximum of 150 hectares of wheat and his crop rotation schedule requires that he plants...
During the past year, Cindy McGill planted a new vineyard on 150 acres of land that...
During the past year, Cindy McGill planted a new vineyard on 150 acres of land that she leases for $31,860 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation. The vineyard will bear no grapes for the first 5 years (1–5). In the next 5 years (6–10), Cindy estimates that the vines will bear grapes that can be sold for $63,530 each year. For the next 20 years (11–30),...
During the past year, Julia McGill planted a new vineyard on 150 acres of land that...
During the past year, Julia McGill planted a new vineyard on 150 acres of land that she leases for $30,090 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation. The vineyard will bear no grapes for the first 5 years (1–5). In the next 5 years (6–10), Julia estimates that the vines will bear grapes that can be sold for $61,290 each year. For the next 20 years (11–30),...
During the past year, Julia McGill planted a new vineyard on 150 acres of land that...
During the past year, Julia McGill planted a new vineyard on 150 acres of land that she leases for $30,920 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation. The vineyard will bear no grapes for the first 5 years (1–5). In the next 5 years (6–10), Julia estimates that the vines will bear grapes that can be sold for $64,360 each year. For the next 20 years (11–30),...
During the past year, Cindy McGill planted a new vineyard on 150 acres of land that...
During the past year, Cindy McGill planted a new vineyard on 150 acres of land that she leases for $31,840 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation. The vineyard will bear no grapes for the first 5 years (1–5). In the next 5 years (6–10), Cindy estimates that the vines will bear grapes that can be sold for $64,820 each year. For the next 20 years (11–30),...
During the past year, Stacy McGill planted a new vineyard on 150 acres of land that...
During the past year, Stacy McGill planted a new vineyard on 150 acres of land that she leases for $30,000 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation. The vineyard will bear no grapes for the first 5 years (1–5). In the next 5 years (6–10), Stacy estimates that the vines will bear grapes that can be sold for $60,000 each year. For the next 20 years (11–30),...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT