TheInnatPennhotelhas400roomswithstandardqueen-sizebedsandtworates:afullpriceof$320and a discount price of $150. To receive the discount price, a customer must purchase the room atleast two weeks in advance (this helps to distinguish between leisure travelers, who tend to bookearly,andbusinesstravelers,whovaluetheflexibilityofbookinglate).ForaparticularTuesdaynight,thehotelestimatesthatthedemandfromleisuretravelerscouldfillthewholehotelwhilethedemandfrombusinesstravelersisdistributednormallywithameanof250roomsandastandarddeviationof100.

Due to customer no-shows, The Inn at Penn hotel is considering implementing overbooking.Theforecast of no-shows is expressed by the discrete probability distribution below.F(Y) represents thecumulative probability distribution of no-shows. The Inn is sensitive about the quality of service itprovides alumni, so it estimates the cost of failing to honor a reservation is $400 in lost goodwill andexplicitexpenses.

What is the optimal overbooking limit, that is, the maximum reservations above the available 400roomsthatTheInnshouldaccept?

Providetheanalysisthrougha"stand-alone"Excelxlsxfile.YoumustsubmittheExcelfilewithproperformulasandinput data intoget credit.

Y	F(Y)	Y	F(Y)	Y	F(Y)
0	0.01	6	0.24	12	0.67
1	0.05	7	0.28	13	0.72
2	0.09	8	0.30	14	0.80
3	0.15	9	0.40	15	0.88
4	0.20	10	0.50	16	0.95
5	0.22	11	0.53	17	1.00