Question

A hotel has 100 rooms. It can charge 400 – 3.5x dollars per room per night when a rooms are occupied. What level of occupancy brings in the most revenue for a night?

Answer 1

To find the level of occupancy that brings in the most revenue for a night, we need to determine the value of x that maximizes the revenue function. By taking the derivative of the revenue function and setting it equal to zero, we find that around 57 rooms occupied will bring in the most revenue.

Step-by-step explanation:

To determine the level of occupancy that brings in the most revenue for a night, we need to find the revenue function based on the given information.

The revenue generated by the hotel can be calculated using the formula R = (400 - 3.5x) * x, where x represents the number of rooms occupied.

To find the level of occupancy that maximizes the revenue, we need to determine the value of x that maximizes the revenue function.

To do this, we can take the derivative of the revenue function with respect to x and set it equal to zero. Solving this equation will give us the value of x that maximizes the revenue. We can then substitute this value back into the revenue function to find the maximum revenue.

By solving the equation, we find that x = 57.14, which means that around 57 rooms occupied will bring in the most revenue for a night.