The grimsley inn has 250 rooms and the standard rate is $150 per night per room. During the non-holiday season, 100 rooms are booked each day on average. But, for each $20 price reduction, 25 more rooms will be rented. What non-holiday price should be advertised?

Question

superhelp101 · Answer

@aum @freckles

superhelp101 · Answer

@jim_thompson5910

aum · Answer

Assume price reduction of n * 20.
Rate per night = 150 - 20n
Number of rooms booked = 100 + 25n

Total revenue R = (150 - 20n) * (100 + 25n)
Maximize R.

Find dR/dn, equate to zero and solve for n.

ganeshie8 · Answer

or simply find the vertex of quadratic

ganeshie8 · Answer

they tricky part is setting up revenue function as u can see

superhelp101 · Answer

wait, so what do we do with the 250 rooms

aum · Answer

That is a constraint on the max rooms that can be rented.

aum · Answer

100 + 25n <= 250

superhelp101 · Answer

lol what does that mean?

aum · Answer

n <= 6.

superhelp101 · Answer

is it possible to have 250 instead of 25 ?

aum · Answer

When finding the "n" that gives maximum revenue, if n exceeds 6, then you have to stop at n = 6.

superhelp101 · Answer

okay it's making a bit more sense. But I am not completing understanding how we got 100+25n

aum · Answer

"for each $20 price reduction, 25 more rooms will be rented."
If price reduces by 20*n, then 25*n more rooms will be rented.  
"More" here refers to more than average number of rooms rented when the rate is standard.  That is 100 rooms + 25*n rooms.

superhelp101 · Answer

oh okay

superhelp101 · Answer

Thank you!

aum · Answer

You are welcome.