Question

A large hotel finds that it can rent 95 rooms when it charge $100 per room. For each $1 increase in room cost it rents one room less. (Likewise, for each $1 decrease in room cost it rents one room more) What price should it charge in order to maximize the revenue?

Answer 1

an interesting question
he gains 99 for the extra room but loses 95 for the rooms he used to charge at 100
so he only gains 4 for each extra drop in price
at 95 cost *100 rooms =income is 9500
at100cost*95 rooms =income is 9500
he makes a few dollars more between these but is it worth the trouble/

Answer 2

This can be expressed by the equation below:

Amount of revenue obtained, y = -a^2 - 5a + 9500 (where a is an integer ≥ 0).
To find the maximum value of y, you would simply need to find the max turning point of this curve.

Answer 3

You'll have to derive this equation yourself; it can be done quite simply from the original question. Try it out and you should be able to do it.