A hotel has 210 units. All rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant. Each occupied room costs $24 per day to service and maintain. What should the hotel charge per day in order to maximize daily profit

Step-by-step explanation:

Given

There are 210 units of hotel

Each room charge $90 when fully occupied

occupied room charges is $24 per day

Suppose x rooms are vacant, so, there 210-x occupied

Daily expense on maintenance

Earning from 210-x rooms

Profit(P)=Earning - Expense

To get the maximum profit, determine the derivative of P w.r.t. x and equate it to zero

Charges for maximum profit is

Number of occupied rooms are