As the manager of a 60-unit hotel you know that all units are occupied when you charge $80 a day per unit. Each occupied room costs $8 for service and maintenance a day. In addition there is a fixed cost of $400 a day. You have also observed that for every 2x dollars increase in the daily rate above $80, there are x units vacant.

The owner of the property insists that the profit is maximized when all units are occupied. Is she correct in her assessment?

Compute the level of profit when all units are occupied. If her assertion is wrong compute the maximum possible profit that you can earn for her.

Compute the daily rate that you will charge and the number of units that will be occupied and the units that will remain vacant.

If instead of maximizing profit, the owner wants to maximize sales revenue, decide the daily rate and the number of units that will be occupied. Show and describe all your calculations

(Hint: Decide the demand function for hotel rooms for this hotel)