Question

Park Hyatt Philadelphia at the Bellevue, located at Walnut and Broad in downtown Philadelphia has a capacity of 240 king rooms. Customers of Hyatt are typically either leisure travelers or business customers. Hyatt charges a discount fare of $125 for a midweek stay (but requires booking a week in advance) which contrast the regular fare of $275. Typically, business customers book in the last minute, and are willing to pay the regular fare, if they can be guaranteed accommodation. Suppose we are interested in the bookings in Park Hyatt on August 6th (the day of our final exam). Hyatt knows that there are plenty of leisure travelers, willing to pay the low fares. However, all else being equal, Hyatt would like to fill those rooms with the high-fare travelers. The objective of Hyatt is to maximize the sum of revenue from both sections of the travelers. If Hyatt followed the ‘booking limit policy’, by reserving some rooms for last-minute business customers, how many rooms should it reserve? Assume that there is ample demand of leisure customers willing to pay the discount fare, and the number of business customers is normally distributed, with mean 50 and standard deviation 26. (6 points)

Answer 1

`X=53`

Explanation:

From the question we are told that:

Regular fare R= $275

Discount fare of $125

Mean
`\=x =50`

Standard deviation
`\sigma= 26.`

Generally, the equation for Critical Fraction is mathematically given by

`C=(Pf-Pd)/(Pf)`

`C=(275-125)/(275)`

`C=0.5`

From Z Distribution Table

`Z=0.1131`

Therefore

Reservation made is give as for High fare travellers is

`X = \=x+(z* \sigma)`

`X = 50 + (0.1131 * 26)`

`X=53`