Gce Model Questions Vol1 2017 Geography Question 43

A farmer has 10 ha of arable land. The baseline yield without inputs is 2.5 t ha⁻¹. Fertiliser applied uniformly at \(F\) kg ha⁻¹ increases yield by 0.4 t per 50 kg ha⁻¹, up to a maximum increase of 1.2 t ha⁻¹. Irrigation can be installed on any integer number \(I\) of hectares (0 ≤ \(I\) ≤ 10) at a cost of £500 per hectare; it adds 0.3 t ha⁻¹ to the yield on the irrigated hectares but reduces the effective fertiliser‑yield increase by 20 % on all land. Fertiliser costs £0.30 per kg. The farmer may spend at most £12 000 on fertiliser and irrigation combined. The market price of the crop is £200 per tonne and there are no other costs. Determine the combination of fertiliser application (in kg ha⁻¹) and irrigated hectares that maximises the farmer's annual profit, and state the maximum profit (in £).