A 300 room hotel is filled to capacity at \$80 a night. If the charge is increased by \$3 it rents 9 less rooms. If it costs \$10 to clean a rented room the next day, how much should the inn keeper charge in order to maximize its profit?
I thought the question was really straight forward and that I'd be able to do the following to get my answer:
Revenue = (# Of Rooms * Room Charge) - (# Of Rooms * Clean Charge)
Revenue = (300 * 80) - (300 * 10) which is 24,000 - 3,000 so Revenue = \$21,000
Not Full Inn
Revenue = (291 * 83) - (291 * 10) which is 24,153 - 2,910 so Revenue = \$21,243
Therefore the inn keeper should charge \$83 a room. I got the question wrong, so can someone explain what I should have done?