Chapter 2.B, Problem 79E

Fertilizing Winter Wheat. Guidelines for the amount of supplementary nitrogen needed to grow winter wheat depend on the amount of nitrogen in the soil (as determined by a soil test), the price of fertilizer, and the price of wheat at harvest. Suppose the soil on a particular farm has a nitrogen content of 2 ppm (parts per million) and 50 acres will be planted in wheat. Consider two pricing scenarios.

• Case A: The price of fertilizer is $0.25/lb, the price of wheat is $3.50/bushel, and the expected yield is 60 bushels/acre.

• Case B: The price of fertilizer is $0.50/1b, the price of wheat is $4.50, and the expected yield is 50 bushels/acre.

In Case A, the guidelines recommend adding 100 pounds of nitrogen per acre, and, in Case B, 70 lbs of nitrogen should be added per acre.

Assuming all other factors are equal, compute and compare the net profit (income minus expenses) for the two scenarios.