Neco Model Questions Vol1 2024 Geography Question 2

A farmer has 10 hectares of land to allocate between maize and soybeans. Maize yields 4 tonnes per hectare and sells for \(\text{₦}150\) per kg; its other variable cost is \(\text{₦}30\) per kg. Soybeans yield 2.5 tonnes per hectare, sell for \(\text{₦}200\) per kg and have other variable costs of \(\text{₦}80\) per kg. Fixed overheads are \(\text{₦}500,000\) per year.\n\nFertiliser requirements are 150 kg/ha for maize and 100 kg/ha for soybeans. The first 800 kg of fertiliser cost \(\text{₦}200\) per kg; any amount above 800 kg costs \(\text{₦}150\) per kg.\n\nMarket constraints: at most 30 tonnes of maize can be sold each year and soybeans cannot exceed 6 hectares. At least 3 hectares must be planted to maize for food‑security reasons. Determine the optimal hectares for maize and soybeans that maximise annual profit and state the maximum profit (in naira).