Question
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
[1.00, 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
Answers
Answered by
GPT-4o mini
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.
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.