The marginal cost of producing the xth box of computer disks is $2 + \frac { x ^ { 2 } } { 120,000 }$ and the fixed cost is $120,000. Find the cost function $C ( x )$ .
A) $C ( x ) = 2 x + \frac { x ^ { 3 } } { 360,000 } - 120,000$
B) $C ( x ) = 2 x + \frac { x ^ { 3 } } { 360,000 } + 120,000$
C) $C ( x ) = - 2 x + \frac { x ^ { 3 } } { 360,000 } + 120,000$
D) $C ( x ) = \frac { x ^ { 3 } } { 360,000 } - 120,000$
E) $C ( x ) = \frac { x ^ { 3 } } { 360,000 } + 120,000$

Question

The marginal cost of producing the xth box of computer disks is $2 + \frac { x ^ { 2 } } { 120,000 }$ and the fixed cost is $120,000. Find the cost function $C ( x )$ .  
A) $C ( x ) = 2 x + \frac { x ^ { 3 } } { 360,000 } - 120,000$
B) $C ( x ) = 2 x + \frac { x ^ { 3 } } { 360,000 } + 120,000$
C) $C ( x ) = - 2 x + \frac { x ^ { 3 } } { 360,000 } + 120,000$
D) $C ( x ) = \frac { x ^ { 3 } } { 360,000 } - 120,000$
E) $C ( x ) = \frac { x ^ { 3 } } { 360,000 } + 120,000$

Quizplus · Accepted Answer

The cost function $C(x)$ is found by integrating the marginal cost function and then adding the fixed cost. Integrating $2 + \frac{x^2}{120,000}$ gives $2x + \frac{x^3}{360,000}$. Adding the fixed cost of $120,000 results in $C(x) = 2x + \frac{x^3}{360,000} + 120,000$.

The Marginal Cost of Producing the Xth Box of Computer 2+x2120,0002 + \frac { x ^ { 2 } } { 120,000 }2+120,000x2​

The Marginal Cost of Producing the Xth Box of Computer $2 + \frac { x ^ { 2 } } { 120,000 }$