Question

Suppose a hotel operator finds that they can fill 119 rooms at a nightly price of $285 and 128 rooms at a nightly price of $259. Assuming that the demand function is linear, find the nightly price which maximizes nightly revenue.  Hint: Recall that revenue = price times quantity.

Answer 1

Price equation:

we are given points as

(x,p)=(119,285)

(x,p)=(128,259)

Firstly, we will find slope

now, we can use point slope form of line

we can solve for p

Revenue:

we can find revenue

R(x)=xp

we can find derivative

now, we can set it to 0

and solve for x

we get

we can find price

.........Answer