Neco 2018 Geography Question 16

A textile manufacturer is evaluating two possible sites for a new factory. Site A: fixed annual cost ₦2,000,000; variable production cost ₦150 per unit; distance to raw‑material source 40 km (transport cost ₦5 per km per unit); distance to market 60 km (transport cost ₦8 per km per unit). Site B: fixed annual cost ₦1,500,000; variable production cost ₦180 per unit; distance to raw‑material source 20 km (same transport cost); distance to market 90 km (same transport cost). Assuming each unit requires one unit of raw material, let \(Q\) denote the annual number of units produced. (a) Derive the total annual cost functions for Site A and Site B in terms of \(Q\). (b) Find the break‑even production quantity at which the two total‑cost functions are equal (round to the nearest whole unit). (c) If the factory plans to produce 3,500 units per year, state which site yields the lower total cost.