5. Cost, Revenue, and Break-Even

Running a small business means comparing what you spend to what you earn.

• Cost combines fixed costs (rent, equipment) and variable cost per item:
  \[ C = (\text{fixed}) + (\text{cost per item}) \times x. \]
• Revenue is the price per item times the number sold:
  \[ R = (\text{price}) \times x. \]
• Profit is revenue minus cost: \(\text{Profit} = R - C\).

The break-even point is where revenue equals cost (profit is zero).

Worked example: A vendor pays $200 for a booth (fixed) plus $3 to make each bracelet, and sells each for $7. Set revenue equal to cost:
\[ 7x = 200 + 3x. \]
Subtract \(3x\): \(4x = 200\), so \(x = 50\) bracelets. Selling 50 bracelets covers all costs; every bracelet after that is profit.

Worked example (profit): If the vendor sells 80 bracelets, profit is \(R - C = 7(80) - (200 + 3 \cdot 80) = 560 - 440 = 120\) dollars.