A line graph shows revenue y = 400x and cost y = 200x + 600. At what quantity x do revenue and cost break even?

A line graph shows revenue y = 400x and cost y = 200x + 600. At what quantity x do revenue and cost break even?

• A. 2
• B. 3
• C. 4
• D. 5

Answer: (B)

Break-even happens when revenue equals cost. Set 400x equal to 200x + 600 and solve for x: subtract 200x from both sides to get 200x = 600, then divide by 200 to find x = 3. So at a quantity of 3 units, the revenue and the cost are both 1200 (revenue 400×3 = 1200; cost 200×3 + 600 = 1200).

Break-even happens when revenue equals cost. Set 400x equal to 200x + 600 and solve for x: subtract 200x from both sides to get 200x = 600, then divide by 200 to find x = 3. So at a quantity of 3 units, the revenue and the cost are both 1200 (revenue 400×3 = 1200; cost 200×3 + 600 = 1200).