A company's average cost per unit when *x* units are produced is defined to be

Average cost =

Total cost

*x*

.

Suppose a company's average costs are given by

Average cost =

5000/*x* + 75 + 0.8*x*.

The company's average cost per unit formula is given by:

\[
\text{Average Cost} = \frac{\text{Total Cost}}{x}
\]

where \( x \) is the number of units produced.

In this case, the average cost function is already provided as:

\[
\text{Average Cost} = \frac{5000}{x} + 75 + 0.8x
\]

This function gives the average cost of producing \( x \) units, where:
- \( \frac{5000}{x} \) represents the fixed costs distributed over \( x \) units,
- \( 75 \) is a constant cost per unit,
- \( 0.8x \) is the variable cost that increases with each additional unit produced.

### Further Questions:
1. What is the total cost function based on the given average cost function?
2. How does the average cost change as \( x \) increases?
3. What is the minimum average cost and at what production level does it occur?
4. How would the average cost function change if the fixed cost was increased to \( 6000 \)?
5. How does the variable cost \( 0.8x \) affect the overall cost as production scales?

**Tip**: The total cost function can be derived by multiplying the average cost by \( x \), giving insight into the cost behavior as production changes.

A company's average cost per unit when x units are produced is defined to be Average cost = Total cost / x. Suppose a company's average costs are given by Average cost = 5000/x + 75 + 0.8x.

Explore how to calculate the average cost of producing x units using the formula Average Cost = 5000/x + 75 + 0.8x. This detailed explanation covers algebraic cost function analysis, optimization, and provides insights into the impact of variable costs. Suitable for high school students in Grades 11-12.

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