Define the decision variables and state objective function

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Reference no: EM13918947

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 con- vention 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 re- quest 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 Sat- urday night only reservation. Thus, six types of reservations are possible: Convention customers/two-night package; convention customers/Friday night only; convention cus- tomers/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-NightPackage	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	Friday Night	Saturday Night
	Package	Only	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.

a. Define the decision variables and state the objective function.

b. Formulate a linear programming model for this revenue management application.

c. What are the optimal allocation and the anticipated total revenue?

d. 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 accept- ing this additional reservation?

TABLE 5.11 RETURNS OVER FIVE 1-YEAR PERIODS FOR SIX MUTUAL FUNDS

Mutual Funds Large-Cap Stock	Year 1 35.3	Year 2 20.0	Year 3 28.3	Year 4 10.4	Year 5 -9.3
Mid-Cap Stock	32.3	23.2	-0.9	49.3	-22.8
Small-Cap Stock	20.8	22.5	6.0	33.3	6.1
Energy/Resources Sector	25.3	33.9	-20.5	20.9	-2.5
Health Sector	49.1	5.5	29.7	77.7	-24.9
Technology Sector	46.2	21.7	45.7	93.1	-20.1
Real Estate Sector	20.5	44.0	-21.1	2.6	5.1

Reference no: EM13918947

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