Waec Model Questions Vol1 2023 Agricultural Science Question 5

A farmer cultivates sorghum and cowpea on a total of 10 ha of land. The expected yields (kg per ha) are 30 kg of sorghum and 20 kg of cowpea. After government policies, the net price of sorghum becomes ₦70 /kg (original ₦80 /kg minus a ₦10 /kg export tax) and the net price of cowpea becomes ₦125 /kg (original ₦120 /kg plus a ₦5 /kg import tariff). Fixed production costs are ₦500 per ha for sorghum and ₦400 per ha for cowpea. Because of market saturation, the profit from each crop decreases with the area planted: - Sorghum profit (in ₦) = 2000 x - 150 x², where x is the area (ha) planted to sorghum. - Cowpea profit (in ₦) = 2500 y - 200 y², where y is the area (ha) planted to cowpea. If x + y = 10, determine the land allocation (ha) to sorghum and to cowpea that maximises total profit. Give the answer to two decimal places.