Break-Even Quantity from Fixed Cost

Equation: at break-even, revenue equals total cost: p·Q = F + v·Q, so Q = F / (p − v). Values: F = $30,000 is the fixed cost, where the total-cost line meets the dollar axis. p = $80/unit is the selling price, the slope of the revenue line. v = $50/unit is the variable cost, the slope of the total-cost line. Step 1: contribution per unit, p − v = 80 − 50 = $30. Step 2: Q = 30,000 / 30 = 1,000 units. Dividing by the price alone gives 375 units, and dividing by the variable cost gives 600 units, which ignores the revenue side.