Break-Even Analysis

Business Calculus · Axiom Academy

Finding when revenue equals cost - the point where profit begins You're opening a coffee shop. Your monthly costs are: Fixed costs: 3,000/month (rent, utilities, insurance) Variable costs: 2 per cup of coffee (beans, cups, labor) You plan to sell each cup for 5 . The Question: How many cups must you sell each month to break even (where total revenue equals total cost)? Let q = number of cups sold per month What is the Revenue function R(q)? Step 2: Find the Break-Even Point At break-even, Revenue = Cost: Solve for q. What is the break-even quantity? Step 3: Visualize the Break-Even Point Below 1,000 cups: Loss (Cost > Revenue) At exactly 1,000 cups: Break-even (Cost = Revenue) Above 1,000 cups: Profit (Revenue > Cost) At the break-even point (q = 1,000 cups): Example: If you sell 1,500 cups:

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