Solve the Problem $C(x)=100,000+20 x+\frac{x^{2}}{10,000}$ , Where $x$ Is the Number of Graphing Calculators Manufactured

Multiple Choice

Solve the problem.
-The cost function for the manufacture of graphing calculators is given by $C(x) =100,000+20 x+\frac{x^{2}}{10,000}$ , where $x$ is the number of graphing calculators manufactured. Using the appropriate domain, sketch the graph of the average cost $\bar{C}$ to manufacture $x$ graphing calculators. What is the significance of $\lim _{x \rightarrow \infty} \bar{C}$ ?

A) $\begin{gathered}\lim \bar{C}=43.27 \\ x \rightarrow \infty\end{gathered}$ . This means that as the production level increases, the average cost per calculator increases to a maximum of $\$ 43.27$ .
B) $\underset{x \rightarrow \infty}{\lim \bar{C}=0}$ . This means that as the production level increases, the average cost per calculator approaches 0 .
C) $\underset{x \rightarrow \infty}{\lim } \bar{C}=+\infty$ . This means that as the production level increases, the average cost per calculator increases without bound.
D) $\lim _{x \rightarrow \infty} \bar{C}$ does not exist.