A company increases the price of its product from $50 to $60, resulting in a price elasticity of demand of -2. If the company's fixed costs are $10,000 and the variable cost per unit is $30, how many units must they sell to break even after the price increase?

To find the break‑even quantity, set total revenue equal to total cost. The revenue is the new price times the quantity sold, so \(60Q\). The total cost is the fixed cost plus the variable cost per unit times the quantity, \(10{,}000 + 30Q\). Setting them equal gives \(60Q = 10{,}000 + 30Q\). Solving for \(Q\) yields \(30Q = 10{,}000\), so \(Q = 333.