Neco Model Questions Vol1 2020 Geography Question 36

A farmer plans to produce maize. The average annual rainfall in his area is 1200 mm. The expected yield per hectare (in tons) from maize is modeled by \( Y = 1.5 + 0.002R + 0.04F - 0.00005F^{2} \), where \(R\) is the rainfall in mm and \(F\) is the amount of fertilizer (kg ha\(^{-1}\)) applied uniformly over the cultivated land. The farmer has a total of 10 000 kg of fertilizer and is limited by a regulation that no more than 150 kg ha\(^{-1}\) may be applied. He wishes to obtain at least 30 tons of maize. Determine the minimum land area (in hectares, to two decimal places) he must cultivate to meet the target, assuming he uses the same fertilizer rate on all the land and does not exceed the regulation.