Break-even and Profit Sensitivity for a Restaurant

Context

A restaurant has fixed monthly costs (rent, salaries) and a variable cost per customer (food, payment processing). Each customer generates a certain average revenue. You are asked to compute break-even volume and analyze how profit changes when costs or revenue change.

Assume the following concrete numbers for this exercise:

• Fixed costs F = $5,000 per month
• Variable cost per customer v = $8
• Revenue per customer p = $20
• Monthly volume to evaluate profit n = 600 customers

Tasks

1. Write the profit function P(n) in terms of p, v, F, and n. Compute the break-even customer count n*.
2. Compute the baseline monthly profit at n = 600 customers.
3. Re-compute profit at n = 600 and the new break-even point in each scenario: a) Fixed costs drop by $600 (F decreases by$ 600). b) Variable cost per customer drops by $1 (v decreases by$ 1). c) Revenue per customer drops by $1.50 (p decreases by$ 1.50).
4. Briefly explain the business implications of (a), (b), and (c).

Hint: Profit = Revenue − Cost, and the contribution margin per customer is (p − v).