Question

If
C(x)
is the cost of producing x units of a commodity, then the average cost per unit is
c(x) =
C(x)
x
.
Consider the cost function
C(x)
given below. (Round your answers to the nearest cent.)
C(x) = 54,000 + 240x + 4x^(3/2)

Answer 1

To find the average cost per unit \( c(x) \), we first need to compute the total cost function \( C(x) \), which is already given:

\[
C(x) = 54,000 + 240x + 4x^{3/2}
\]

The average cost per unit \( c(x) \) is defined as:

\[
c(x) = \frac{C(x)}{x}
\]

Now, let’s substitute \( C(x) \) into this equation:

\[
c(x) = \frac{54,000 + 240x + 4x^{3/2}}{x}
\]

We can simplify this expression by dividing each term in the numerator by \( x \):

\[
c(x) = \frac{54,000}{x} + 240 + \frac{4x^{3/2}}{x}
\]

This simplifies to:

\[
c(x) = \frac{54,000}{x} + 240 + 4x^{1/2}
\]

The average cost function \( c(x) \) now has three components:

1. \( \frac{54,000}{x} \) - The fixed cost per unit.
2. \( 240 \) - The variable cost per unit.
3. \( 4x^{1/2} \) - The additional variable cost based on the square root of the number of units produced.

You can also find specific values for \( c(x) \) for particular values of \( x \) if needed. If you have any specific values of \( x \) to evaluate, please provide them. Otherwise, this is the general formulation for the average cost per unit.