Gce Model Questions Vol1 2017 Agricultural Science Question 22

An agricultural extension officer has a total budget of ₦500 000 for a programme. The programme consists of two activities:\n\n1. A farmer‑training component. Each farmer who attends a workshop incurs a variable cost of ₦2 500 (materials, venue) and a follow‑up visit costing ₦1 200. Every farmer must receive exactly one follow‑up visit.\n\n2. A radio‑broadcast component. The cost is ₦5 000 for every 1 000 listeners reached.\n\nA 10 % administrative overhead is applied to the total variable cost of the farmer‑training component (i.e. 10 % of the sum of the workshop and follow‑up costs for all farmers).\n\nThe officer must serve at least 50 farmers. Determine the combination of the number of farmers served (\(n\)) and the number of listeners reached (in thousands, \(m\)) that maximises the total number of beneficiaries (farmers + listeners) while staying within the budget. State the optimal values of \(n\) and the total number of listeners (not in thousands).