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:
- \( \frac{54,000}{x} \) - The fixed cost per unit.
- \( 240 \) - The variable cost per unit.
- \( 4x^{1/2} \) - 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.
12 answers