A hotel rents 240 240 rooms at a rate of $ 40 $40 per day. For each $ 2 $2 increase in the rate, four fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $

The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600

Step-by-step explanation:

Given

First, we calculate the revenue.

Let x be the change in rate.

i.e.

For every 2x increment in price (p) i.e. p + 2x

There will be 4 fewer rooms (n) i.e. n - 4x

So, the revenue is updated as:

So:

So:

Expand

Reorder

The maximum of a function is calculated as:

In:

So:

To get the maximum revenue;

Substitute 40 for x in

The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600

28

step-by-step explanation:

8+8+6+6