Question

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.

Answer 1

The net profit or income for case A and case B based on the information will be $9250 and $9500 respectively.

How to compute the net profit?

Case A:

Based on the information, the price of fertilizer will be:

= 0.25 × 100 × 50

= $1250

Price of wheat = 3.50 × 50 × 50

= $10500

Net profit = $10500 - $1250

= $9250

Case B:

Price of fertilizer will be:

= 0.50 × 70 × 50

= $1750

Price of wheat = 4.50 × 50 × 50

= $11250

Net profit = $11250 - $1750

= $9500

Therefore, the net profit or income for case A and case B based on the information will be $9250 and $9500 respectively.

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