Question

your turn!
choose the option that best answers the question.
a company is planning to manufacture cell phones. the fixed monthly cost will be $1,200,000 and it will cost $329 to produce each phone. what is the horizontal asymptote for the graph of the average cost function, c, of producing x phones?
a. c has no horizontal asymptote
b. y = 329

Explanation:

Step1: Find the average cost function

The total cost function \(T(x)=1200000 + 329x\). The average cost function \(C(x)=\frac{T(x)}{x}=\frac{1200000}{x}+329\).

Step2: Find the limit as \(x\to\infty\)

We calculate \(\lim_{x
ightarrow\infty}C(x)=\lim_{x
ightarrow\infty}(\frac{1200000}{x}+329)\).
Since \(\lim_{x
ightarrow\infty}\frac{1200000}{x} = 0\) (using the rule \(\lim_{x
ightarrow\infty}\frac{a}{x}=0\) for \(a\) - constant), then \(\lim_{x
ightarrow\infty}C(x)=0 + 329\).

Answer:

B. \(y = 329\)