Question

41. Rou Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Business Rental Class Super Saver Deluxe $30 $35 $20 $30 Room Type I Type II $40 Type I rooms do not have high-speed Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. a. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental class not satisfied? Explain. b. How many reservations can be accommodated in each rental class?

Answer 1

Answer(a): Using Linear programming, let us calculate the number of reservations to accept in each rental class:

             For the Class 1 rental =
f 21,"22)
= $C^{_{1}}X^{_{_{1}}}$ + $C^{_{2}}X^{_{_{2}}}$

> f (100 x 0.01) = 100 + 100

> f 1 = 200

>f = 200

& For the Class II rental =  
f 21,"22)
= $C^{_{1}}X^{_{_{1}}}$ + $C^{_{2}}X^{_{_{2}}}$

> f (120 x 0.01) = 120 + 120

> f 1.2= 240

>f = 166

Answer (b): For the First rental class, the total accomodation of rental rooms would be :

(130 + 60 + 50) - 200

> 240 - 200 = 40

i.e. 200 out of the 240 reservations can be made.

& For the Second rental class, the total accomodation of rental rooms would be :

(130 + 60 + 50) - 166

> 240 - 166 = 74

i.e. 166 out of the 240 reservations can be made.

Answer (c): The consideration of the management to offer free breakfast to the people who upgrade from Super Saver to Delux rooms at the cost of $5 can only be fruitful or executed only if the total benefit derived out of the offer made increased the number of upgraders which would directly increase the profit margin for the hotel and therefore prove t be beneficial for the hotel.

Answer (d) : If we have to choose from the two types of rooms for the upgraded room from the office, then we would want to prefer the Type II room, This is because, it is expected that more people would want to opt for the lesser rental room with the high speed internet service, and there is more probability for the Type II room to be getting an additional room for the consumers.

Answer (e): In order to use the linear model to accomodate the information for the next night, the primary information required would be the preference level of the consumers to choose the same or the different type of rental rooms after spending a night in their first perefered rentl room. Once we have the data of the preference of the consumers for the next night, the limear programming model can then be used in order to derive the expected allocation of demanf for the rental rooms for the next night.