Hello,

I assume:

a) that each room is rented for $90

b) that the price could be increased by multiple of $5:

let x be the times that the price is increased:

let i be the income:

i(x) = (72 - 2x)(90 - 5x) = -10x² + 180x + 6480

The original situation is i(0) = $6480

The graph of this function is a parabola opening downward so the maximum value is at it's vertex. Use derivation:

i'(x) = -20x + 180. You'll get the maximum if i'(x) = 0 ==> x = 9

i(9) = $7290 when only 72 - 18 = 54 rooms are rented for a price of $(90-5*9) = $45