a certain company has a fixed cost of $200 per day. it costs the company $3.10 per unit to make its…

Explanation:

Step1: Recall asymptote concepts

For a rational function $f(x)=\frac{a + bx}{x}=\frac{a}{x}+b$ (where $a = 200$, $b = 3.10$), vertical asymptotes occur where the denominator is zero, and horizontal asymptotes are determined by the behavior as $x\to\pm\infty$.

Step2: Find vertical asymptote

Set the denominator of $f(x)=\frac{200 + 3.10x}{x}$ equal to zero. So $x = 0$ is the vertical - asymptote. But this has nothing to do with the average cost approaching a value as the number of units produced increases.

Step3: Find horizontal asymptote

As $x\to\pm\infty$, $\lim_{x\to\pm\infty}\frac{200+3.10x}{x}=\lim_{x\to\pm\infty}(\frac{200}{x}+3.10)$. Since $\lim_{x\to\pm\infty}\frac{200}{x}=0$, then $\lim_{x\to\pm\infty}\frac{200 + 3.10x}{x}=3.10$. This means the average cost per unit will approach $$3.10$ as the number of units produced increases.

Answer:

The horizontal asymptote of $y = 3.10$ represents that the average cost per unit will approach $$3.10$ as the number of units produced increases.