determining horizontal asymptotes\na small manufacturer constructs refrigerators. the fixed monthly cost is…

determining horizontal asymptotes\na small manufacturer constructs refrigerators. the fixed monthly cost is $200,000, and it costs $450 to produce one refrigerator. the average cost function to produce x refrigerators is represented by:\nc̅(x) = (200,000 + 450x)/x\nwhat is the horizontal asymptote of c̅(x)?\ny =
Answer
Answer:
$y = 450$
Explanation:
Step1: Simplify the cost - function
$\overline{C}(x)=\frac{200000 + 450x}{x}=\frac{200000}{x}+450$
Step2: Find the limit as $x\to\pm\infty$
$\lim_{x\to\pm\infty}\overline{C}(x)=\lim_{x\to\pm\infty}(\frac{200000}{x}+450)$ Since $\lim_{x\to\pm\infty}\frac{200000}{x}=0$, then $\lim_{x\to\pm\infty}(\frac{200000}{x}+450)=450$. So the horizontal asymptote is $y = 450$.