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According to data from the United States According to the National Agricultural Statistics Service of the United States Department of Agriculture, 124 million acres of land in the United States were used for wheat or corn farming in a recent year. Farmers used 50 million of those 124 million acres to grow $2.158 billion bushels of wheat and 74 million acres to grow$11.807 billion bushels of corn. Assume that wheat and corn farming in the United States is productive. At that point in production, the opportunity cost of producing one additional bushel of wheat is $1.7 bushels of corn less. However, because farmers' opportunity costs are increasing, additional bushels of wheat have a higher opportunity cost than1.71.7bushels of corn.Determine whether each of the following production points is I feasible and efficient in production, (ii) feasible but inefficient in production, (iii) not feasible, or (iv) unclear as to whether or not it is feasible. a. Farmers cultivate 40 million acres of land to produce$1.8 billion bushels of wheat and 60 million acres of land to cultivate 9 billion bushels of corn. The remaining 24 million acres are underutilised. b. Farmers convert 40 million acres of corn land to wheat production from their original production point. They currently produce $3.158 billion bushels of wheat and$10.107 billion bushels of corn. c. Farmers reduce wheat production to 2 billion bushels while increasing corn production to 12.044 billion bushels. The opportunity cost of moving from $11.807 billion bushels of corn to$12.044 billion bushels of corn along the production possibility frontier is $0.666 bushel of wheat per bushel of corn.

Question

Growing Degree Days The number of growing degree days (GDD) is the sum, over all days in a year in which the temperature is above 40F40^{\circ} \mathrm{F}, of the amount that the temperature exceeds 40F40^{\circ} \mathrm{F}. It can be approximated by

f(x,y)=3652πx3652(40y)+365(40y)2πxf(x, y)=\frac{365}{2 \pi} x-\frac{365}{2}(40-y)+\frac{365(40-y)^2}{\pi x}

where xx is the difference in degrees F\mathrm{F} between the average temperature in July and the average temperature in January, and yy is the average of those two temperatures.
a. The average January temperature in New York City is 32F32^{\circ} \mathrm{F}, and the average July temperature is 77F77^{\circ} \mathrm{F}. Use the formula above to approximate the number of GDD. Compare this value with the average of 5945 calculated at www. yourweekendview.com/outlook/agriculture/growingdegree-days/USNY0996.
b. For New York City, find the rate of change of the number of GDD with respect to the average of January and July temperatures if the difference between those averages remains constant.
c. For New York City, find the rate of change of the number of GDD with respect to the difference between average January and July temperatures if the average between those remains constant.
d. Find the average January and July temperature for your home town and compute the number of GDD. Then compare with the actual number from the website given in part a.

Solution

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(a)

The average in January is 3232, and the average in July is 7777. The difference between them is

x=7732=45x = 77-32 = 45

The average value is

y=32+772=1092=54.5y = \frac{32+77}{2} = \frac{109}{2} = 54.5

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