Question

Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. The Classic Corvette Owners Association scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are possible: convention customers/two-night package; convention customers/Friday night only; convention customers/Saturday night only; regular customers/two-night package; regular customers/Friday night only; and regular customers/Saturday night only.

The cost for each type of reservation is shown here:

	Two-Night Package	Friday Night Only	Saturday Night Only
Convention	$225	$123	$130
Regular	$295	$146	$152

The anticipated demand for each type of reservation is as follows:

	Two-Night Package	Friday Night Only	Saturday Night Only
Convention	40	20	15
Regular	20	30	25

Hanson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize total revenue.

1. Define the decision variables and state the objective function. Round your answers to the nearest whole number.
   

   Let	CT = number of convention two-night rooms
   	CF = number of convention Friday only rooms
   	CS = number of convention Saturday only rooms
   	RT = number of regular two-night rooms
   	RF = number of regular Friday only rooms
   	RS = number of regular Saturday only room

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

2. Formulate a linear programming model for this revenue management application. Round your answers to the nearest whole number. If the constant is "1" it must be entered in the box.
   

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

   S.T.

   1)	CT
   2)	CF
   3)	CS
   4)	RT
   5)	RF
   6)	RS
   7)	CT	+	CF
   8)	CT	+	CS
   9)	CT	+	CF	+	RT	+	RF
   10)	CT	+	CS	+	RT	+	RS
   11)	CT,	CF,	CS,	RT,	RF,	RS			0

3. What are the optimal allocation and the anticipated total revenue? Round your answers to the nearest whole number.
   

   Variable	Value
   CT
   CF
   CS
   RT
   RF
   RS

   
   Total Revenue = $  
   
4. Suppose that one week before the convention the number of regular customers/Saturday night only rooms that were made available sell out. If another nonconvention customer calls and requests a Saturday night only room, what is the value of accepting this additional reservation? Round your answer to the nearest dollar.
   
   The dual value for constraint 10 shows an added profit of $   if this additional reservation is accepted.

Answer 1