A notebook cost 150 if you buy 20, 130 if you buy 15 and 110 if 12. Calculate the total cost of 10 notebooks. solve piecewise function

To calculate the total cost of 10 notebooks using a piecewise function, we must determine how the price per notebook changes depending on the quantity purchased. Let's define the piecewise function based on the given dataTo calculate the total cost of 10 notebooks using a piecewise function, we must determine how the price per notebook changes depending on the quantity purchased. Let's define the piecewise function based on the given 

- \( p(q) = 150 \) if \( q \geq 20 \)
- \( p(q) = 130 \) if \( 15 \leq q < 20 \)
- \( p(q) = 110 \) if \( 12 \leq q < 15 \)

Where:
- \( p(q) \) is the price per notebook when buying \( q \) notebooks.

Since you want to calculate the total cost for 10 notebooks, observe that 10 is less than 12. Since the pricing is only given for quantities 12 or more, we cannot directly use the provided price points. However, typically, for quantities less than the minimum threshold, the price would stay at the highest price given.

Therefore, the piecewise function can be extended as:
- \( p(q) = 150 \) if \( q \geq 20 \)
- \( p(q) = 130 \) if \( 15 \leq q < 20 \)
- \( p(q) = 110 \) if \( 12 \leq q < 15 \)
- \( p(q) = p_{base} \) for \( q < 12 \) where \( p_{base} \) is some baseline price, presumably 150 in this context since it's the highest price.

Given the assumption:
- \( p(q) = 150 \) for \( q < 12 \)

### Calculation
The cost of 10 notebooks would be:
\[
\text{Total Cost} = 10 \times 150 = 1500
\]

So, the total cost of 10 notebooks is **1500**.

Would you like more details, or do you have any questions?

### Related Questions
1. What if the baseline price for quantities less than 12 was 130 instead of 150?
2. How would the cost change if you were purchasing 14 notebooks?
3. What is the total cost for 25 notebooks?
4. How would you express this piecewise function if additional price tiers were introduced?
5. Can the pricing model be represented using a step function?
6. How would a bulk discount affect the pricing model?
7. What assumptions are made in extending the piecewise function to quantities below 12?
8. How do price variations influence consumer purchasing decisions in bulk buying?

### Tip
When working with piecewise functions, always carefully examine the different intervals and corresponding function definitions to avoid mistakes in application.

Learn how to calculate the total cost of notebooks using a piecewise function. Understand the pricing tiers and how to apply them to different quantities of notebooks. Suitable for advanced high school students.

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