Gce Model Questions Vol1 2024 Commerce Question 2

A retailer buys 200 units of a product. The purchase price (excluding freight) is \(\£P\). Freight adds 5% of \(\£P\). The retailer marks the product up by 30% on the purchase price (excluding freight) to obtain the full selling price. A seasonal discount of 12% is offered on the selling price, and a trade‑in allowance of \(\£15\) per unit is given to customers who return an old appliance (the allowance is added to the revenue). The profit per unit sold at the full price is therefore \(\£0.25P/200\). The retailer wants a total profit of \(\£3000\) from this batch. Assuming the purchase price is \(\£10\,000\), what is the minimum number of units that must be sold at the discounted price (with the trade‑in allowance) in order to reach the profit target? Show all steps.