Question

In: Math

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 for wheat. If the market price is $225 per acre for corn and $100 per acre for wheat, how many acres of each crop should she plant in order to maximize her revenue?

A.

1. Set up a linear programming problem, choosing variables, finding a formula for your objective function, and inequalities to represent the constraints.

2. You will need to decide a reasonable range for your variables, and then put in a column of values within that range for the x-variable in column A. Then you want to solve each constraint equation for y, and use that formula to get values in the "y for C1", etc., columns (B, C, D). Then graph the three constraint lines on one graph (as you did in Lab 1: open its Word document if you need refreshing on how to do this).

3. Shade in the feasible region.

4. Find the corners of the feasible region using goal seek to find intersections of lines, as you did in Lab 1.

5. Find in column H the values of f at the corners of the feasible region.

6. Determine the maximum revenue.

7. Finally, using new objective functions for when the prices of corn are at their highs and lows, answer the final question. This only involves computing new values of the objective function, not any new graphing or constraints.

x represents:

y represents:

Formula for objective function: f =

Constraint 1:

Constraint 2:

Constraint 3:

Corners of feasible region f at corners

So how many acres of each crop should she plant?

Expert Solution

milcah answered 1 year ago

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 farmer has 1000 acre of land on which he can grow corn, wheat and soyabeans....

A farmer has 1000 acre of land on which he can grow corn, wheat and soyabeans. Each acre of corn cost Rs. 100 for preparation, requires 7 man days of work and yields a profit of Rs. 30. An acre of wheat cost Rs. 120 for preparation, requires 10 man days of work and yields a profit of Rs. 40. An acre of soyabeans cost Rs. 70 to prepare, requires 8 man days of work and yields a profit of...

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 Brown planted com and wheat on his 1120 acres of land. The cost of planting and harvesting corn (which includes seed, planting, fertilizer, machinery, labor and other costs) is $270 per acre

Farmer Brown planted com and wheat on his 1120 acres of land. The cost of planting and harvesting corn (which includes seed, planting, fertilizer, machinery, labor and other costs) is $270 per acre. The cost of planting and harvesting what is $140 por acre. If Farmer Brown's total cost was $237,400, how many acres of com did he plant? Farmer Brown planted _______ acres of com

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...

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...

Your farm encompasses 500 acres, and you are planning to grow soybeans, corn, and wheat in...

Your farm encompasses 500 acres, and you are planning to grow soybeans, corn, and wheat in the coming planting season. Fertilizer costs per acre are: $5 for soybeans, $2 for corn, and $1 for wheat. You estimate that each acre of soybeans will require an average of 5 hours of labor per week, while tending to corn and wheat will each require an average of 2 hours per week. Based on past yields and current market prices, you estimate a...

A farmer needs to decide which type of corn he wants to plant. To decide, he...

A farmer needs to decide which type of corn he wants to plant. To decide, he plants two small test areas. After the corn has grown he compares the lengths of the cobs. He looks at 35 cobs of Type A, which had an average length of 6.3 inches with a variance of 1. He looks at 30 cobs of Type B, which had an average length of 5.9 with a variance of 1.3. Calculate a 95% confidence interval for...

Ida is a freelance artist. She purchased 10 acres of land in 2013. The land was...

Ida is a freelance artist. She purchased 10 acres of land in 2013. The land was held by Ida as investment property. On July 1, 2018, the land was condemned by the county government to build a new courthouse and jail facility. The county awarded Ida $550,000 for the condemnation of the land. Ida used the full amount of the proceeds to purchase a building that she will use as a production studio for her artwork. The reinvestment occurred within...

Suppose a country uses Land to produce either wheat or corn. Each unit of Land produces...

Suppose a country uses Land to produce either wheat or corn. Each unit of Land produces either 3 Corn or 4 Wheat. The country has 1200 units of land. a) What is the opportunity cost of corn? b) If the country produces 2400 Wheat, how much Corn can they produce? c) If they increase Corn production by 300 how much will they reduce Wheat production? d) Is the combination 1500 units of Corn and 3200 units of Wheat Efficient, Inefficient...