A farmer grows cassava with fixed costs of $150,000$ ₦ per season and variable costs of $45,000$ ₦ per hectare. Expected yield is 12 tonnes per hectare. The market price is $12,000$ ₦ per tonne, but for each hectare above 5 ha the price falls by 5 % per extra hectare (price = $12,000$ ₦ × (1 - 0.05 × (H - 5)) for H  5). The farmer can cultivate up to 10 ha. Determine the number of hectares that maximizes profit and state the maximum profit (in ₦).

Question

A farmer grows cassava with fixed costs of $150,000$ ₦ per season and variable costs of $45,000$ ₦ per hectare. Expected yield is 12 tonnes per hectare. The market price is $12,000$ ₦ per tonne, but for each hectare above 5 ha the price falls by 5 % per extra hectare (price = $12,000$ ₦ × (1 - 0.05 × (H - 5)) for H > 5). The farmer can cultivate up to 10 ha. Determine the number of hectares that maximizes profit and state the maximum profit (in ₦).

Accepted Answer

9 hectares; maximum profit = 481,800 ₦

Neco 2018 Agricultural Science Question 15

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