<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 A certain product's per-unit selling price $P$ (in yuan) over the past $30$ days is a function of time $t$ (in days) as follows: $P = \begin{cases} t+20 & 0 < t < 25, t \in \mathbb{N}_+ \\ -t+100 & 25 \leq t \leq 30, t \in \mathbb{N}_+ \end{cases}$. The daily sales volume $Q$ (in units) of this product is a function of time $t$ (in days) as follows: $Q = -t + 40$ $(0 < t \leq 30, t \in \mathbb{N}^*)$. Calculate the maximum daily sales revenue for this product. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
1125
A certain product's per-unit selling price $P$ (in yuan) over the past $30$ days is a function of time $t$ (in days) as follows: $P = \begin{cases} t+20 & 0 < t < 25, t \in \mathbb{N}_+ \\ -t+100 & 25 \leq t \leq 30, t \in \mathbb{N}_+ \end{cases}$. The daily sales volume $Q$ (in units) of this product is a function of time $t$ (in days) as follows: $Q = -t + 40$ $(0 < t \leq 30, t \in \mathbb{N}^*)$. Calculate the maximum daily sales revenue for this product.
test