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 to make a profit of
$190/acre on Crop A and $230/acre on Crop B, how
many acres of each crop, x and y, respectively,
should she plant to maximize her profit P in dollars?
| Maximize | P | = | subject to the constraints | ||
| cost | |||||
| labor | |||||
| x ≥ 0 | |||||
| y ≥ 0 | |||||
Homework Answers
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Formulate but do not solve the following exercise as a linear
programming problem.
A farmer plans...
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...
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 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...
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...
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 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...
Formulate but do not solve the following exercise as a linear programming problem. Anander plans to...
Formulate but do not solve the following exercise as a linear programming problem. Anander plans to invest up to $500,000 in two projects Project A yields a return of on the investment of dollars, whereas Project yields a return of 13 on the investment of y dollars. Because the investment in Project is riskler than the investment in Project A, the financer has decided that the investment in Project should not exceed 40% of the total investment. How much should...
Formulate but do not solve the following exercise as a linear programming problem A company manufactures...
Formulate but do not solve the following exercise as a linear programming problem A company manufactures x units of product A, y units of product, and units of product C Each product is processed in three departments: I, I, and TIL The total available labor hours per week for Departments I, II, and I are 920, 2000, and 310, respectively. The time requirements in hours per unit and profit per unit for each product are as follows. Product Product Product...
Problem 1-1 A farmer owns 450 acres of land. He is going to plant each acre...
Problem 1-1 A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $4000 profit, requires three workers, and requires two tons of fertilizer. Each acre planted with corn yields $2000 profit, requires two workers, and requires four tons of fertilizer. There are currently 1000 workers and 1200 tons of fertilizer available. To hedge against risk, the farmer wants to sure that the acres of wheat do...
A) Formulate but do not solve the following exercise as a linear programming problem. Madison Finance...
A) Formulate but do not solve the following exercise as a linear programming problem. Madison Finance has a total of $18 million earmarked for homeowner loans and auto loans, where x is homeowner loans in millions of dollars and y is auto loans in millions of dollars. On the average, homeowner loans have a 10% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans...
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 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...
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...
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...
Formulate but do not solve the following exercise as a linear programming problem. Anander plans to invest up to $500,000 in two projects Project A yields a return of on the investment of dollars, whereas Project yields a return of 13 on the investment of y dollars. Because the investment in Project is riskler than the investment in Project A, the financer has decided that the investment in Project should not exceed 40% of the total investment. How much should...
Formulate but do not solve the following exercise as a linear programming problem A company manufactures x units of product A, y units of product, and units of product C Each product is processed in three departments: I, I, and TIL The total available labor hours per week for Departments I, II, and I are 920, 2000, and 310, respectively. The time requirements in hours per unit and profit per unit for each product are as follows. Product Product Product...
Problem 1-1 A farmer owns 450 acres of land. He is going to plant each acre with wheat or corn. Each acre planted with wheat yields $4000 profit, requires three workers, and requires two tons of fertilizer. Each acre planted with corn yields $2000 profit, requires two workers, and requires four tons of fertilizer. There are currently 1000 workers and 1200 tons of fertilizer available. To hedge against risk, the farmer wants to sure that the acres of wheat do...
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