Neco Model Questions Vol1 2022 Geography Question 2

A farmer wants to maximise wheat yield per hectare. The yield (tons/ha) is modelled by \[Y = 2 + 0.04F - 0.0001F^{2} + 0.009R - 0.000005R^{2} + 0.5P,\] where \(F\) is fertilizer applied (kg/ha), \(R\) is average rainfall (mm) and \(P\) is a pest‑control index (0-5). The region's baseline figures are \(F=120\) kg/ha, \(R=800\) mm and \(P=2\).\n\nThe farmer can spend a total of \(30\,000\) Naira on improvements, choosing any combination of the following options (each option may be used up to its stated limit):\n- Increase fertilizer by up to 100 kg/ha at \(10\) Naira per kg.\n- Increase rainfall by up to 100 mm at \(5\) Naira per mm (through irrigation).\n- Increase the pest‑control index by 1 unit at \(2\,000\) Naira per unit (maximum increase of 2 units).\n\nDetermine the combination of improvements that gives the highest possible wheat yield and state that maximum yield (rounded to two decimal places).