Waec Model Questions Vol1 2024 Agricultural Science Question 20

A farmer has 10 ha of land to allocate between maize and soybeans. The profit (in naira) from each crop is given by \[\pi_m = \bigl(p_m\,y_m - C_m\bigr)A_m,\qquad \pi_s = \bigl(p_s\,y_s - C_s\bigr)A_s,\] where \(A_m\) and \(A_s\) are the areas (ha) planted to maize and soybeans respectively (\(A_m+A_s=10\)). The parameters are: - Maize: price \(p_m = 45{,}000\) ₦ ton⁻¹, yield \(y_m = 2.5 - 0.1A_m\) ton ha⁻¹, total cost per ha \(C_m = 10{,}000 + 2{,}000A_m\) ₦. - Soybeans: price \(p_s = 60{,}000\) ₦ ton⁻¹, yield \(y_s = 1.8 - 0.05A_s\) ton ha⁻¹, total cost per ha \(C_s = 8{,}000 + 1{,}500A_s\) ₦. Determine the allocation of land (values of \(A_m\) and \(A_s\) to two decimal places) that maximises total profit \(\Pi = \pi_m+\pi_s\), and state the maximum profit (rounded to the nearest naira).