Piecewise and greatest Integer function. f(×)=[1.50, 0<×<10,000

[1.00, 10,000< × < 30,000
[0.85, 30,000< × < 45,000 × is the number of units produced a day and f(×) is cost per unit of the production..Give me a answer to correctly interprets this function

1 answer

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:

  1. 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.
  2. 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.
  3. 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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