Neco 2022 Agricultural Science Question 28

A farmer grows cassava on one hectare. Fixed cost for the season is \(\text{₦}120,000\) and the variable cost (excluding fertilizer) is \(\text{₦}30,000\) per hectare. Yield (tonnes per hectare) depends on the amount of fertilizer applied, \(x\) kg/ha, according to \(Y = 10 + 0.2x\) (tonnes), but yield cannot exceed 15 t/ha. The market price per tonne is \(\text{₦}20,000\) when the yield is 10 t/ha; for each additional tonne produced the price falls by 3 % of the original price. Fertilizer costs \(\text{₦}2,000\) per kg. Profit per hectare is revenue minus all costs. What amount of fertilizer (in whole kilograms) should be applied to maximise profit, and what is the maximum profit (rounded to the nearest naira)?