Marcy Hotel is a boutique hotel in Boston downtown area. The operations manager, Jenna, needs your help to decide how many rooms (of a particular type) to book for a day. The nightly stay in these rooms is $200 and the hotel has 100 of those rooms. The data shows that some customers do not show-up. To protect against no show-ups, Jenna is considering to book more than 100 rooms per night. Although this practice allows Jenna to utilize each room available as much as possible, it comes with a risk. The risk is that if Jenna books more than 100 rooms and if more customers than expected show-up, then some customers will not be able to stay at the hotel even though they made a reservation. To protect those customers, Marcy Hotel is providing a compensation of 120% of the booking price paid by the customer. Also, any no show-up customer Is refunded 30% of the booking price paid by the customer.

How many rooms should Jane book in a day to maximize its expected revenue? Answer this question by developing a simulation optimization model using R. In your model, assume that the number of no-shows is normally distributed with a mean of (0.2*number of rooms booked) and standard deviation of (0.05*number of rooms booked).