Neco Model Questions Vol1 2025 Agricultural Science Question 45

A farmer produces maize. The total cost (in thousand naira) of producing \(Q\) tonnes is \(C(Q)=0.02Q^{2}+5Q+200\). The market price per tonne follows the linear demand function \(P=120-0.1Q\). The farmer may also sell a fixed quantity of \(Q_{0}=200\) tonnes to a contract buyer at a guaranteed price of ₦80 000 per tonne, incurring no additional cost. (a) If the farmer sells all his output to the market, determine the quantity \(Q\) that maximises profit and compute the maximum profit. (b) If the farmer sells exactly \(Q_{0}=200\) tonnes to the contract buyer and any remaining output \((Q-Q_{0})\) to the market, find the optimal total production \(Q\) and the corresponding maximum profit. Which overall strategy yields the higher profit, and what is that profit (in thousand naira)?