Suppose a manufacturer has determined that the total cost C of operating a factory is $C = 0.6 x ^ { 2 } + 14 x + 54,000$ where $x$ is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is $\mathrm { C } / x$.)
A) $x = 300$ units
B) $x = 330$ units
C) $x = 30$ units
D) $x = 60$ units
E) $x = 600$ units

Question

Suppose a manufacturer has determined that the total cost C of operating a factory is $C = 0.6 x ^ { 2 } + 14 x + 54,000$ where $x$ is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is $\mathrm { C } / x$.) 
A) $x = 300$ units
B) $x = 330$ units
C) $x = 30$ units
D) $x = 60$ units
E) $x = 600$ units

Quizplus · Accepted Answer

To minimize the average cost per unit, we need to find the value of $x$ that minimizes the function $AC = \frac{C}{x} = 0.6x + 14 + \frac{54000}{x}$. Taking the derivative and setting it to zero gives $x = 300$.

Suppose a Manufacturer Has Determined That the Total Cost C C=0.6x2+14x+54,000C = 0.6 x ^ { 2 } + 14 x + 54,000C=0.6x2+14x+54,000

Suppose a Manufacturer Has Determined That the Total Cost C $C = 0.6 x ^ { 2 } + 14 x + 54,000$