Question Detail
Question
If the average cost per unit atom is given by the function C(q) = 1000 - 24q + q², where q is the mass produced. What unit of mass will minimize the average cost per unit?
Correct Answer
Option B is the correct answer.
Detailed Explanation
To find the minimum average cost, we need to find the derivative of C(q) with respect to q and set it to zero.C(q) = q² - 24q + 1000C'(q) = dC/dq = 2q - 24Set C'(q) = 0: 2q - 24 = 0 => 2q = 24 => q = 12.To confirm it's a minimum, find the second derivative: C''(q) = d²C/dq² = 2. Since C''(q) = 2 > 0, the cost is minimized at q = 12.
Hint
To find the minimum value of a function, take its first derivative and set it to zero. Use the second derivative test to confirm it's a minimum.