A farmer has 150 acres of land suitable for cultivating Crops A and B. The cost of cultivating Cr...
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 $150/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?
$ _____
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A farmer has 150 acres of land suitable for cultivating Crops A and B. The cost of cultivating Cr...
Formulate but do not solve the following exercise as a linear programming problem. A farmer plans...
Formulate but do not solve the following exercise as a linear programming problem. A farmer plans to plant two crops, A and B. The cost of cultivating Crop A is $40/acre, whereas the cost of cultivating Crop B is $60/acre. The farmer has a maximum of $7200 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 2900 labor-hours available. If she expects...
A fruit grower has 150 acres of land available to raise two crops, A and B
A fruit grower has 150 acres of land available to raise two crops, A and B. It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B, and there are 240 days available each year for trimming. It takes 0.3 days to pick an acre of crop A and 0.1 days to pick an acre of crop B, and there are 30 days per year available for picking. The profit...
please write step by step. thank you. 4-28. A farmer has subdivided his land into three...
please write step by step. thank you.
4-28. A farmer has subdivided his land into three plots and wants to plant three crops in each plot: corn, rice, and soy. Plot sizes, crop acreage, profit per acre, and manure needed (pounds per acre) are given in the table at the bottom of this page. The maximum acreage for each crop denotes the total acres of that crop that can be planted over all three plots. Currently there are 450,000 pounds...
A farmer in the Midwest has 1,000 acres of land on which she intends to plant...
A farmer in the Midwest has 1,000 acres of land on which she intends to plant corn, wheat, and soybeans. Each acre of corn costs $100 for preparation, requires 7 worker-days of labor, and yields a profit of $30. An acre of wheat costs $120 to prepare, requires 10 worker-days of labor, and yields $40 profit. An acre of soybeans costs $70 to prepare, requires 8 worker-days, and yields $20 profit. The farmer has taken out a loan of $80,000...
A farmer is going to divide her 50 acre farm between two crops. Seed for crop...
A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs $50 per acre. Seed for crop B costs $25 per acre. The farmer can spend at most $2000 on seed. If crop B brings in a profit of S50 per acre, and crop A brings in a profit of $130 per acre, how many acres of each crop should the farmer plant to maximize her profit'? Preview acres of crop A acres...
A farmer owns 450 acres of land. He is going to plant each acre with wheat...
A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $2000 profit, requires three workers and requires two tons of fertilizer. Each acre planted with corn yields $3000 profit, requires two workers, and requires four tons of fertilizer. There are currently 1000 workers and 1200 tons of fertilizer available. The farmer wants to maximize his profit from planting his land. a) Write the managerial formulation for...
A farmer is planning his spring planting. He has 20 acres on which he can plant...
A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available. The following table summarizes the data for the problem. Crop Profit per Acre...
A farmer has 400 acres of available land and $80,000 to spend He wants to plant the combination o...
Please show work using
matrices, thank you!
A farmer has 400 acres of available land and $80,000 to spend He wants to plant the combination of crops which 'maximizes his profit. Complete parts a. through c below Profits and Constraints for Crops Potatoes Corn X2 $128 $40 Cabbage Total Number of Acres Cost (per acre Profit (peracre a. Give tne auai propiem X400 $320 $120 $224 S80,000 $60 2 subject to 320y2 120 128y20 2242 60 with y120, y2 20...
constraint ineanie (5 marks) b) A farm in Kedah has 6000 acres available to plant with rubber tree and oil palms. Each acre of rubber trees requires 9 gallons of fertilizer/herbicide and hour of...
constraint ineanie (5 marks) b) A farm in Kedah has 6000 acres available to plant with rubber tree and oil palms. Each acre of rubber trees requires 9 gallons of fertilizer/herbicide and hour of labor to harvest. Each acre of oil palms requires 3 gallons of fertilizer/herbicide and 1 hour of labor to harvest. The farm has available at most 40,500 gallons of fertilizer/herbicide and at most 5250 hours of labor for harvesting. The profits per acre are RM60 for...
17. A farmer has 100 acres of tillable land on which corn, tomatoes, beans, peas, and...
17. A farmer has 100 acres of tillable land on which corn, tomatoes, beans, peas, and carrots can be planted. The labor requirements, plant costs, and gross income for I acre of each of these crops are as follows: Labor Gross (worker-hours) Costs (S) Income (S) Corn 95 1300 275 345 435 20 200 Tomatoes Beans Peas Carrots 120 25 35 40 75 nd The farmer has available up to 3600 hr of labor at $7.25/hr. However, the labor and...
please write step by step. thank you.
4-28. A farmer has subdivided his land into three plots and wants to plant three crops in each plot: corn, rice, and soy. Plot sizes, crop acreage, profit per acre, and manure needed (pounds per acre) are given in the table at the bottom of this page. The maximum acreage for each crop denotes the total acres of that crop that can be planted over all three plots. Currently there are 450,000 pounds...
A farmer in the Midwest has 1,000 acres of land on which she intends to plant corn, wheat, and soybeans. Each acre of corn costs $100 for preparation, requires 7 worker-days of labor, and yields a profit of $30. An acre of wheat costs $120 to prepare, requires 10 worker-days of labor, and yields $40 profit. An acre of soybeans costs $70 to prepare, requires 8 worker-days, and yields $20 profit. The farmer has taken out a loan of $80,000...
A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs $50 per acre. Seed for crop B costs $25 per acre. The farmer can spend at most $2000 on seed. If crop B brings in a profit of S50 per acre, and crop A brings in a profit of $130 per acre, how many acres of each crop should the farmer plant to maximize her profit'? Preview acres of crop A acres...
Please show work using
matrices, thank you!
A farmer has 400 acres of available land and $80,000 to spend He wants to plant the combination of crops which 'maximizes his profit. Complete parts a. through c below Profits and Constraints for Crops Potatoes Corn X2 $128 $40 Cabbage Total Number of Acres Cost (per acre Profit (peracre a. Give tne auai propiem X400 $320 $120 $224 S80,000 $60 2 subject to 320y2 120 128y20 2242 60 with y120, y2 20...
constraint ineanie (5 marks) b) A farm in Kedah has 6000 acres available to plant with rubber tree and oil palms. Each acre of rubber trees requires 9 gallons of fertilizer/herbicide and hour of labor to harvest. Each acre of oil palms requires 3 gallons of fertilizer/herbicide and 1 hour of labor to harvest. The farm has available at most 40,500 gallons of fertilizer/herbicide and at most 5250 hours of labor for harvesting. The profits per acre are RM60 for...
17. A farmer has 100 acres of tillable land on which corn, tomatoes, beans, peas, and carrots can be planted. The labor requirements, plant costs, and gross income for I acre of each of these crops are as follows: Labor Gross (worker-hours) Costs (S) Income (S) Corn 95 1300 275 345 435 20 200 Tomatoes Beans Peas Carrots 120 25 35 40 75 nd The farmer has available up to 3600 hr of labor at $7.25/hr. However, the labor and...
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