Final answer:
The break-even level of output is approximately 7.26 units.
Step-by-step explanation:
To find the break-even level of output, we need to set the total cost equal to the total revenue. In this case, the revenue is given by the market price multiplied by the quantity, which is $38Q. The cost function is TC = 6Q² - 12Q + 80. Setting these two equations equal to each other and solving for Q, we can find the break-even level of output:
38Q = 6Q² - 12Q + 80
6Q² - 50Q + 80 = 0
Using the quadratic formula, we can solve for Q:
Q = (-(-50) ± sqrt((-50)^2 - 4(6)(80))) / (2(6))
Q = (50 ± sqrt(2500 - 1920)) / 12
Q = (50 ± sqrt(580)) / 12
Since the break-even level of output cannot be negative, we take the positive root:
Q = (50 + sqrt(580)) / 12 ≈ 7.26
Therefore, the break-even level of output is approximately 7.26 units.