Math Problem Statement
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.
Solution
The company's average cost per unit formula is given by:
where is the number of units produced.
In this case, the average cost function is already provided as:
This function gives the average cost of producing units, where:
- represents the fixed costs distributed over units,
- is a constant cost per unit,
- is the variable cost that increases with each additional unit produced.
Further Questions:
- What is the total cost function based on the given average cost function?
- How does the average cost change as increases?
- What is the minimum average cost and at what production level does it occur?
- How would the average cost function change if the fixed cost was increased to ?
- How does the variable cost affect the overall cost as production scales?
Tip: The total cost function can be derived by multiplying the average cost by , giving insight into the cost behavior as production changes.
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Math Problem Analysis
Mathematical Concepts
Algebra
Cost Functions
Optimization
Formulas
Average Cost = Total Cost / x
Average Cost = 5000/x + 75 + 0.8x
Theorems
Optimization of Functions
Cost Function Analysis
Suitable Grade Level
Grades 11-12
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