ITPEC IP October 2020 Question 68
A restaurant has the total sales, the variable cost, the fixed cost, and the business days per year shown below. In order for the restaurant to make at least 4 million yen in annual profit, what is the minimum number of customers required per business day?
Explanation
40 customers — the contribution of each customer must cover the fixed cost plus the target profit over the year, then spread over 300 business days.
- •Contribution per customer: 3,000 − 1,000 = 2,000 yen
- •Contribution needed per year: 20 million + 4 million = 24 million yen
- •Customers per year: 24,000,000 ÷ 2,000 = 12,000
- •Customers per business day: 12,000 ÷ 300 = 40
Answer (d)
Why not others:
- •(a) 14 and (b) 20 — too few: 20 customers a day bring 20 × 300 × 2,000 = 12 million yen a year, not even the fixed cost, and 14 bring less
- •(c) 27 — divides by the sales per customer, 24,000,000 ÷ 3,000 = 8,000 a year and 8,000 ÷ 300 ≈ 26.7, forgetting that 1,000 yen of each sale goes to variable cost
Key rule: Required quantity = (fixed cost + target profit) ÷ contribution per unit, where contribution is price minus variable cost, never the price itself.
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