Neco 2023 Agricultural Science Question 29

A farmer is choosing between two crops for a 5\,ha farm.\nCrop A (maize): variable cost \(\text{₦}20,000\) ha⁻¹, fixed cost \(\text{₦}30,000\) ha⁻¹, expected yield 4 t ha⁻¹. The market price per ton follows a normal distribution with mean \(\text{₦}25,000\) and standard deviation \(\text{₦}5,000\).\nCrop B (soybean): variable cost \(\text{₦}15,000\) ha⁻¹, fixed cost \(\text{₦}40,000\) ha⁻¹, expected yield 2.5 t ha⁻¹. The market price per ton has mean \(\text{₦}30,000\) and standard deviation \(\text{₦}4,000\).\nAssuming profit = revenue - total cost and using a 95 % confidence level (≈1.96 σ), determine which crop provides the higher minimum expected profit at the 95 % confidence level for the whole 5 ha farm, and state that minimum profit.