When Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is...

When Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 -N/200 bushels of corn. If the price of corn is $4 per bushel and the price of fertilizer is $1.20 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

Solutions

Expert Solution

Substitute the given values in the following identity to calculate the value of $\mathrm{N}$ as follows:

$$ \frac{M P_{F}}{M P_{C}}=\frac{P_{F}}{P_{C}} $$

This can be done as follows:

$$ \begin{aligned} \frac{M P_{F}}{M P_{C}} &=\frac{P_{F}}{P_{c}} \\ \frac{(1-N / 200) M P}{M P_{C}} &=\frac{1.20}{4} \\ 1-N / 200 &=0.3 \\ 1-0.3 &=N / 200 \\ 0.7 &=N / 200 \\ & N=140 \end{aligned} $$

Thus, the farmer should use 140 pounds of fertilizer per acre in order to maximize his profits.

Rahul Sunny answered 2 years ago

Next > < Previous

Related Solutions

Part a A farmer applies 1705 kg of a fertilizer that contains 10.0% nitrogen to his...

Part a A farmer applies 1705 kg of a fertilizer that contains 10.0% nitrogen to his fields each year. Fifteen percent (15.0%) of the fertilizer washes into a river that runs through the farm. If the river flows at an average rate of 0.315 cubic feet per second, what is the additional concentration of nitrogen (expressed in milligrams of nitrogen per liter) in the river water due to the farmer's fertilizer each year? Answer: ? mg/L Part b Heptane and...

Using a recommended rate of 175 lbs N/acre (196 kg N/ha), develop a nitrogen fertilizer application...

Using a recommended rate of 175 lbs N/acre (196 kg N/ha), develop a nitrogen fertilizer application for your 1.2m x 6.25m plot. How much more N fo you need to apply if 1 kg ammonium sulfate is applied to an area of 1.2m x 30m? How much ammonium sulfate (21-0-0), complete fertilizer (14-14-14) or Sustane organic fertilizer (4-6-4) do you still need to apply to meet the remaining N requirements?

On a 100-acre farm, a farmer is able to produce 3,000 bushels of wheat when he...

On a 100-acre farm, a farmer is able to produce 3,000 bushels of wheat when he hires 2 workers. He is able to produce 4,400 bushels of wheat when he hires 3 workers. Which of the following possibilities is consistent with the property of diminishing marginal product? Group of answer choices The farmer is able to produce 5,600 bushels of wheat when he hires 4 workers. The farmer is able to produce 5,400 bushels of wheat when he hires 4...

Crop yields per acre depend on many variables, but two obvious ones are fertilizer and weed...

Crop yields per acre depend on many variables, but two obvious ones are fertilizer and weed control. In an effort to test the effects of various levels of fertilizer and of herbicide, researchers selected six plots of land and subdivided each into eight pieces. Each of the eight pieces of each plot was treated with one of the eight combinations of fertilizer (none, light, moderate, heavy) and herbicide (none, some). The per acre yields of each piece of land are...

Crop yields per acre depend on many variables, but two obvious ones are fertilizer and weed...

The average production of peanuts in Virginia is 3000 pounds per acre. A new plant food...

The average production of peanuts in Virginia is 3000 pounds per acre. A new plant food has been developed and is tested on 59 individual plots of land. The mean yield with the new plant food is 3093 pounds of peanuts per acre, and the population standard deviation is 578 pounds. At a = 0.01, can you conclude that the average production has increased? I don't understand how to work this problem.

1) A farmer finds that if she plants 60 trees per acre, each tree will yield...

1) A farmer finds that if she plants 60 trees per acre, each tree will yield 40 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 2 bushels. How many trees should she plant per acre to maximize her harvest? 2)A baseball team plays in a stadium that holds 46000 spectators. With the ticket price at $10 the average attendence has been 19000. When the price dropped to...

Use the crop yields (in pounds per acre) from the samples of regular seed & kiln-dried...

Use the crop yields (in pounds per acre) from the samples of regular seed & kiln-dried seed listed in the table below to answer the following questions. Regular 1903 1935 1910 2496 2108 1961 2060 1444 1612 1316 1511 Kiln Dried 2009 1915 2011 2463 2180 1925 2122 1482 1542 1443 1535 Use an equation editor to formulate the null and alternative hypothesis to test the claim “Kiln dried seed is substantially different than regular seed.” b. Construct a randomization...

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

Assume that the yield per acre for a particular variety of soybeans is N(µ, σ2 )....

Assume that the yield per acre for a particular variety of soybeans is N(µ, σ2 ). For a random sample of n = 10 plots, the yields in bushels per acre were 21.68 33.09 28.20 42.28 44.77 61.97 37.20 55.96 52.18 29.38 i. Give a point estimate for µ and σ. ii. Test you assumption of normality with Q-Q plot. Can you get a another point estimate of σ? iii. Find a 90% confidence interval for µ and an 90%...

Subjects