Neco 2025 Agricultural Science Question 17

In an agricultural extension programme, four villages are to be served. Each extension agent can work with up to 30 farmers per month. The probability that a farmer adopts a new technology when served by the first agent in a village is \(0.60\). For each additional agent assigned to the same village, the adoption probability per farmer decreases by \(0.05\) due to overlap. Each agent costs \(20{,}000\) Naira per month and the total monthly budget is \(120{,}000\) Naira. The target is to have at least 150 farmers adopt the technology in one month. Determine the minimum number of agents to hire and a feasible allocation of agents to the four villages that meets the target while staying within budget. State the allocation (agents per village) and the expected total number of adopters.