Gce Model Questions Vol1 2024 Commerce Question 1

A company plans an advertising campaign using two media: TV and online. Each TV spot costs \(\£2000\) and reaches 5000 viewers. Due to diminishing returns, each additional TV spot reaches only 80% of the viewers reached by the previous spot. Each viewer has a 0.1% chance of making a purchase. Online advertising costs \(\£0.10\) per click, and each click converts to a sale with probability 2%. The profit per unit sold is \(\£25\). The company currently sells 800 units per month with a profit of \(\£6000\). It wants to increase its monthly profit by at least \(\£4000\). Determine the minimum number of TV spots (an integer \(t\ge 1\)) and the minimum number of online clicks (an integer \(c\)) required to achieve this profit increase. Show all reasoning steps.