Neco 2019 Commerce Question 46

An advertising campaign must reach at least 120,000 unique individuals. A TV spot reaches 8,000 viewers, a radio minute reaches 1,200 listeners, and 10 % of TV viewers also listen to the radio. Let \(t\) be the number of TV spots and \(r\) the number of radio minutes. Determine the combination of \(t\) and \(r\) (both whole numbers) that achieves the required reach at the lowest total cost, where a TV spot costs ₦150,000 each, but any spot beyond the first five receives a 12 % discount; a radio minute costs ₦20,000 each, but minutes beyond the first 30 receive a 15 % discount. Using the cheapest feasible combination, compute the total advertising cost. The company expects the advertising to generate sales equal to 1.8 times the advertising cost and aims for a profit margin of 25 % on those sales. Will the expected profit meet a target profit of ₦500,000? If it does, state by how much the profit exceeds the target; if not, state the additional profit required.