A hotel rents 220 rooms at a rate of $ 40 per day. For each $ 1 increase in the rate, two fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $ .

The rooms should be rented at $75 per day for a maximum income of $11250 per day.

Step-by-step explanation:

If the daily rental is increased by $ x

then

Rental:  R (x )=( 40 + x )  dollars per room-day

Number of rooms rented:  N ( x ) = ( 220 − 2 x )  and

Income:  I ( x ) = ( 40 + x ) ( 220 − 2 x ) =8800+140x-2x²  dollars/day

The maximum will be achieved when the derivative of  I ( x )  is zero.

x=35

so, ($40+$35)=75$per day

 I ( x35) =8800+140(35)-2(35)²= 11250

step-by-step explanation:

(s)he  is right it would be 5.5% because it is smaller than 15.5% or anything smaller than 15.5% in general

x = 2

step-by-step explanation:

if sr parallel to ba then the sides bc and ac are in proportion, that is

= ← substitute values

= ( cross- multiply )

27x = 6(4x + 1)

27x = 24x + 6 ( subtract 24x from both sides )

3x = 6 ( divide both sides by 3 )

x = 2