SOLVE THE BOLD QUESTION #4 !

Your submission should include (1) this document with your answers filled in, and (2) any/all additional files (.R files, .xlsx files, etc.) that you used to find your answers. You must work alone.

Suppose you are running an agricultural processing firm in Wisconsin. Your firm owns two different facilities: an ethanol refinery and a processing plant that produces high fructose corn syrup (HFCS). Both facilities require corn as an input. In addition, your firm owns three plots of land: one in Dane County, one in Rock County, and one in Sauk County. Each plot of land can be used to grow corn that can then be used as an input in either the ethanol refinery or the HFCS plant. Your firm has decided that it is only going to process corn that it has grown itself, but it wants to minimize the costs of transporting corn from its fields to its facilities.

You face several different problems. First, since you do not know how much corn you can expect to harvest from each of the three plots of land, you will need to estimate those numbers based on existing data. Second, you need to decide how much corn to grow on each plot and how much of it will be sent to each processing facility. Finally, you need to decide how many acres to cultivate on each plot of land to produce the quantities of corn you require. This problem set will walk you through solving each of these problems.

INFORMATION

Your ethanol refinery requires exactly 25,000 bushels of corn

Your HFCS plant requires exactly 15,000 bushels of corn

The plot of land in Dane County is 75 acres in size

The plot of land in Rock County is 120 acres in size

The plot of land in Sauk County is 90 acres in size

The cost to transport a bushel of corn between each plot of land and each facility is given in the following table:

Plot of Land	Ethanol Refinery	HFCS Processing Plant
Dane County	$0.05	$0.02
Rock County	$0.07	$0.06
Sauk County	$0.04	$0.12

You have access to three different data sets called dane.csv, rock.csv, and sauk.csv. These files contain corn yield data from a random sample of farms in each respective county. For each farm, you observe corn yield (bushels per acre), the amount of nitrogen fertilizer applied (pounds per acre), the amount of phosphorus fertilizer applied (pounds per acre), and the amount of potassium fertilizer applied (pounds per acre).

For any plot(s) of land you cultivate, you plan to apply 200 pounds of nitrogen per acre, 100 pounds of phosphorus per acre, and 150 pounds of potassium per acre.

QUESTIONS

(Round all answers to nearest whole number.)

Begin by calculating the average per-acre corn yield for each county.

Average yield in Dane County (bushels per acre): ________ (1 pt)

Average yield in Rock County (bu/ac): _______ (1 pt)

Average yield in Sauk County (bu/ac): _______ (1 pt)

Next, estimate the per-acre corn yield you would expect to achieve on each of your plots of land given your planned fertilizer applications.

Dane County (bu/ac): _180___ (2 pts)

Rock County (bu/ac): _____ (2 pts)

Sauk County (bu/ac): _ 220 _____ (2 pts)

Use the answers from question 2 (which, remember, should already be rounded to the nearest whole number) to estimate the total corn production for each of your plots of land if you were to cultivate the entire plot.

Expected production on Dane County plot (bushels): __13500_____ (1 pt)

Expected production on Rock County plot (bushels): _24000______ (1 pt)

Expected production on Sauk County plot (bushels): _19800______ (1 pt)

Next, use your answers from question 3 and the information from earlier in this problem set to solve your firms linear programming problem. You can ignore risk and production uncertainty in this problem. Report your solutions below:

Optimal corn production on Dane County plot (bushels): _______ (1 pt)

Optimal corn production on Rock County plot (bushels): _______ (1 pt)

Optimal corn production on Sauk County plot (bushels): _______ (1 pt)

Corn transported from Dane County plot to ethanol refinery (bushels): _______ (1 pt)

Corn transported from Dane County plot to HFCS plant (bushels): _______ (1 pt)

Corn transported from Rock County plot to ethanol refinery (bushels): _______ (1 pt)

Corn transported from Rock County plot to HFCS plant (bushels): _______ (1 pt)

Corn transported from Sauk County plot to ethanol refinery (bushels): _______ (1 pt)

Corn transported from Sauk County plot to HFCS plant (bushels): _______ (1 pt)

Total transportation cost (dollars): _______ (1 pt)

Finally, use your work and previous answers to calculate the number of acres on each plot of land you plan to cultivate. Report your answers below:

Acres cultivated on Dane County plot: _______ (1 pt)

Acres cultivated on Rock County plot: _______ (1 pt)

Acres cultivated on Sauk County plot: _______ (1 pt)

*** If I cannot find your work for an answer above in an attached file (.R file, .xlsx file, etc.), you will not receive credit for it even if the final number is correct.***