A wheat yield (ton ha⁻¹) can be approximated by the quadratic model $Y = pN - qN^{2}$, where $N$ is the amount of nitrogen fertilizer applied (kg ha⁻¹). Field trials gave $Y = 3.2$ t ha⁻¹ when $N = 60$ kg ha⁻¹ and $Y = 3.6$ t ha⁻¹ when $N = 100$ kg ha⁻¹. The region receives 180 mm of rainfall, which is 20 mm below the optimal 200 mm; each 10 mm deficit reduces the actual yield by 0.1 t ha⁻¹. Determine the nitrogen rate that maximises the actual yield after accounting for the water deficit, and give that maximum actual yield (to two decimal places).

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92 kg ha⁻¹; 3.43 t ha⁻¹

Gce Model Questions Vol1 2023 Geography Question 2

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