This question's explanation and your answers so far.
次の条件で，インターネット上にWebサイトを開設して商品販売を開始した。毎月10万円の利益を上げるためには，Webサイトへの毎月の来訪者は少なくとも何人必要か。ここで，Webサイトへの来訪者は全員がインターネット広告経由で来訪し，購入者は1人当たり1個の商品を購入するものとする。また，条件以外の費用は考慮しないものとする。 〔条件〕
| 項目 | 金額 | |
|---|---|---|
| ① | サーバのレンタル費用 | 5万円/月 |
| ② | インターネット広告費用 | 10円/来訪者 |
| ③ | 商品の販売による利益 | 400円/個 |
| ④ | 来訪者が商品を購入する比率 | 10% |
If you forget to multiply by the 10% ratio of visitors who purchase and mistakenly assume that all visitors buy, the profit per person becomes 400 − 10 = 390 yen, and from 390N − 50,000 = 100,000 you get N ≈ 385. In reality only 10% buy, so this value is too small and is incorrect.
This is the value obtained by mistakenly adding the 10-yen advertising cost to the profit instead of subtracting it, treating the per-person figure as 40 + 10 = 50 yen and computing (100,000 + 50,000) ÷ 50 = 3,000. Advertising is a cost (a negative), so the sign was mistaken, making this incorrect.
If you forget to account for the 10-yen-per-visitor advertising cost (a variable cost) and keep the per-person profit at 40 yen, then from 40N − 50,000 = 100,000 you get N = 3,750. Since 10 yen of advertising cost is incurred for each visitor, failing to subtract it is the error.
正解 Let the number of visitors be N. Since 10% of visitors make a purchase and the profit per item is 400 yen, the profit from product sales is 400 yen × 0.1 × N = 40N yen. On the other hand, advertising costs 10 yen per visitor, so it costs 10N yen. Therefore the net profit per visitor is 40 yen − 10 yen = 30 yen. In addition, the server rental cost of 50,000 yen (a fixed cost) is incurred every month. The condition for earning a monthly profit of 100,000 yen is 30N − 50,000 ≥ 100,000, that is, 30N ≥ 150,000, N ≥ 5,000. The minimum number of visitors needed is 5,000, so the correct answer is “エ”.