QuestionQuestion Owners of a car rental company that charges customers between $\$ 95$ and $\$ 200$ per day have determined that the number of cars rented per day can be modeled by the linear function $n(p)=800-4 p$, where $p$ is the daily rental charge. How much should the company charge each customer per day to maximize revenue? Do not include units or a dollar sign in your answer.
Provide your answer below:

Studdy Solution
Check if the critical point $p = 100$ is within the given price range of $95 to$200.
Since $95 \leq 100 \leq 200$, the critical point is within the range.
Evaluate the revenue function at the endpoints and the critical point to determine the maximum revenue:
$$R(95) = 95 \cdot (800 - 4 \cdot 95) = 95 \cdot 420 = 39900$$
$$R(100) = 100 \cdot (800 - 4 \cdot 100) = 100 \cdot 400 = 40000$$
$$R(200) = 200 \cdot (800 - 4 \cdot 200) = 200 \cdot 0 = 0$$
The maximum revenue occurs at $p = 100$.
The company should charge each customer:
$$\boxed{100}$$