The function \( f(x) \) you've provided is a piecewise function that describes the cost per unit of production based on the number of units produced in a day, denoted by \( x \). Here’s a breakdown of each segment of the function:
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For \( 0 < x < 10,000 \):
- The cost per unit \( f(x) \) is \($1.50\).
- This means that if you produce between 1 and 9,999 units in a day, the cost to produce each unit is $1.50.
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For \( 10,000 \leq x < 30,000 \):
- The cost per unit \( f(x) \) is \($1.00\).
- If you produce between 10,000 and 29,999 units, the cost per unit decreases to $1.00. This reflects economies of scale, where producing more units reduces the cost per unit.
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For \( 30,000 \leq x < 45,000 \):
- The cost per unit \( f(x) \) is \($0.85\).
- When production reaches between 30,000 and 44,999 units, the cost further decreases to $0.85 per unit, indicating even more efficiency in production as volume increases.
Summary Interpretation:
- The function represents a fixed cost per unit of production that decreases as the production volume increases.
- It indicates that producing fewer units results in higher costs per unit, while higher production volumes lead to lower costs.
- This structure may encourage businesses to increase production to benefit from lower costs per unit.
In practical terms, if a producer knows the expected volume of production per day, they can use this function to estimate the cost per unit they will incur based on that volume.
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