Question

In: Statistics and Probability

Avila Hotel has 300 rooms and charges $120 per room. The hotel estimates that the demand...

Avila Hotel has 300 rooms and charges $120 per room. The hotel estimates that the demand for the rooms follows a uniform distribution between 270 and 330 each day. Reservations may be canceled by 6pm with no penalty. The hotel estimates that 3% of the reservations are canceled by 6pm. Hence, the hotel allows

overbooking by 20 room (the hotel allows up to 320 customers to make reservation). When more customers arrive than can be handled (e.g., more than 300 customers), the hotel incurs $200 cost by putting them up at another hotel. The daily operating cost is $25,000, regardless of the number of rooms reserved. Develop a simulation model on Excel with 1000 trials to answer the following questions:

a) What is the average net profit of the hotel?

b) What is the probability of having a net profit more than $8,000?

c) What is the probability of having all the rooms occupied by guest

Expert Solution

Observations are generated using the function randbetween. the syntax is =randbetween(270,330)

The frequency distribution observations thus generated is given above.

estimated that 3% of reservations are cancelled taking that in to consideration while calculating the net profit we have the formulas given below

for bookings upto 300 we calculate the net profit using the formula

=(# booked-3%*#booked)*120-25000

and for the net occupancies greater than 300

Net profit is calculated using the formula =300*120-(#booked-300)*$200-$25000

based on tha above calculations we have the following frequency table for net profit

a) the average net profit is 9224.12

b)Probability of having net profit more than 8000

Out of 1000 trials 729 are having more than net profit 8000 hence the required probability i=729/1000=0.729

c)

Probability of having all the rooms occupied by the guest= Probability of trials having value greater than or equal to 300 =360/1000 according to the above table(Hint: count all thr frequencies above 300)

orchestra answered 1 year ago

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