Question

A 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: c(x)= 200,000+450x/x. What is the horizontal asymptote of C(x)?

Answer 1

Answer: Horizontal asymptote of c(x) is 450.

Step-by-step explanation:

Since we have given that

Cost to produce one refrigerator = $450

Fixed monthly cost = $200,000

So, Average cost function to produce x refrigerators is given by

$c(x)=\dfrac{200000+450x}{x}$

Horizontal asymptote of c(x) would be

$\dfrac{450x}{x}\\\\=450$

Hence, Horizontal asymptote of c(x) is 450.

Answer 2

Answer:

y=450

Step-by-step explanation:

It is given that the fixed monthly cost is $200,000, and it costs $450 to produce one refrigerator.

Total cost of x refrigerator is

$T(x)=200,000+450x$

The average cost function to produce X refrigerators is represented by:

$C(x)=\dfrac{200,000+450x}{x}$

If the degree of numerator and denominator are same, then horizontal asymptote is

$y=\frac{p}{q}$

where, p is the leading coefficient of numerator and q is leading coefficient of denominator.

In the above function leading coefficient of numerator is 450 and leading coefficient of denominator is 1. So, horizontal asymptote is

$y=\frac{450}{1}$

$y=450$

Therefore, the horizontal asymptote of C(x) is y=450.