Question 1167398
You can represent the total cost of the catering service as a **piecewise function**, $C(n)$, of the number of attendees, $n$.

The total cost is calculated by multiplying the cost per head by the number of attendees, $n$, for each range.

Let $n$ be the number of attendees.

## Piecewise Cost Function, $C(n)$

$$
C(n) = \begin{cases} 
150n & \text{if } 0 < n \le 20 \\
130n & \text{if } 21 \le n \le 50 \\
110n & \text{if } 51 \le n \le 100 \\
100n & \text{if } n > 100 
\end{cases}
$$

### Explanation of Each Piece:

1.  **For 20 people or less:**
    The cost is $150$ pesos per head.
    $$C(n) = 150n \quad \text{for } 0 < n \le 20$$

2.  **For 21 to 50 persons:**
    The cost drops to $130$ pesos per head.
    $$C(n) = 130n \quad \text{for } 21 \le n \le 50$$

3.  **For 51 to 100 persons:**
    The cost drops again to $110$ pesos per head.
    $$C(n) = 110n \quad \text{for } 51 \le n \le 100$$

4.  **For 101 or more persons:**
    The cost is the lowest at $100$ pesos per head.
    $$C(n) = 100n \quad \text{for } n > 100$$