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 $f(x)=\frac{a + bx}{x}=\frac{a}{x}+b$ ($a = 200$, $b = 3.10$), vertical asymptotes occur when the denominator is 0. Here, when $x = 0$, the function is undefined, so $x=0$ is a vertical asymptote. Horizontal asymptotes for $y=\frac{a+bx}{x}$ can be found by considering the behavior as $x\to\pm\infty$.

Step2: Analyze 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 $\lim_{x\to\pm\infty}\frac{200}{x}=0$, $\lim_{x\to\pm\infty}(\frac{200}{x}+3.10)=3.10$. The horizontal - asymptote $y = 3.10$ means that as the number of units $x$ produced increases (as $x\to\infty$), the average cost per unit $\frac{200 + 3.10x}{x}$ approaches $3.10$.

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.