A farmer intends to grow soybeans on 5 ha. Fixed costs are: land rent $30{,}000$ N per ha, machinery depreciation $12{,}000$ N (total), and insurance $5{,}000$ N. Variable costs per hectare are: seed $8{,}000$ N, fertilizer $15{,}000$ N and labour $4{,}000$ N. The expected market price is $45{,}000$ N per tonne, but if total production exceeds 12 t the price falls by 10 %.

(a) Assuming the price remains at $45{,}000$ N t⁻¹, determine the minimum average yield per hectare (in tonnes) required to achieve a profit of at least $100{,}000$ N.

(b) If the farmer expands to 6 ha and the yield stays at the regional average of 2.8 t ha⁻¹, will the 10 % price reduction apply? Calculate the resulting profit and advise whether expansion is financially advisable.

Question

A farmer intends to grow soybeans on 5 ha. Fixed costs are: land rent $30{,}000$ N per ha, machinery depreciation $12{,}000$ N (total), and insurance $5{,}000$ N. Variable costs per hectare are: seed $8{,}000$ N, fertilizer $15{,}000$ N and labour $4{,}000$ N. The expected market price is $45{,}000$ N per tonne, but if total production exceeds 12 t the price falls by 10 %.

(a) Assuming the price remains at $45{,}000$ N t⁻¹, determine the minimum average yield per hectare (in tonnes) required to achieve a profit of at least $100{,}000$ N.

(b) If the farmer expands to 6 ha and the yield stays at the regional average of 2.8 t ha⁻¹, will the 10 % price reduction apply? Calculate the resulting profit and advise whether expansion is financially advisable.

Accepted Answer

Minimum yield ≈1.79 t ha⁻¹; profit with 6 ha = 321 400 N, expansion advisable

Gce Model Questions Vol1 2025 Agricultural Science Question 37

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