Question 1167398: The cost of hiring a catering service to serve food for a party is 150 pesos per head for 20 person or less 130 pesos per head for 21 to 50 persons and 110 pesos per head for 51 to 100 person for 100 or more person the cost is the 100 pesos per head represent the total cost as à piece wise function of the number of attendees of the party
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! 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.
$$C(n) = 100n \quad \text{for } n > 100$$
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