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 acres will be planted in winter wheat. Consider two pricing scenarios.
Case​ A: The price of fertilizer is ​$​/lb., the price of wheat is ​$​/bushel, and the expected yield is ​bushels/acre.
Case​ B: The price of fertilizer is ​$​/lb., the price of wheat is ​$​/bushel, and the expected yield is ​bushels/acre.
In Case​ A, the guidelines recommend adding pounds of nitrogen per​ acre, and in Case​ B, pounds of nitrogen per acre. Assuming all other factors are​ equal, compute and compare the net profits​ (income minus​ expenses) for the two scenarios.