8-5 Problem 8-5 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: Rental Class Super Saver Type I Room Type II Delux Business e $30 $35 - $15 $25 $35 Type I rooms do not have wireless 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, 65 rentals in the Deluxe class, and 45 rentals in the Business class. Round Tree has 90 Type I rooms and 130 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. Rental Class with room type No of Reservations Super Saver rentals allocated to room type I 90 Super Saver rentals allocated to room type II 20 Deluxe rentals allocated to room type I 0 Deluxe rentals allocated to room type II 65 Business rentals allocated to room type II 45 Demand by rental class was not satisfied. Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank (b) How many reservations can be accommodated in each rental class? Rental Class No of Reservations Super Saver I 110 Deluxe 65 Business 45 Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered? (c) Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank With a little work, an unused office area could be converted to a rental room. If the (d conversion cost is the same for both types of rooms, would you recommend converting the ) office to a Type I or a Type II room? Type I Shadow Price $ Type II $ Convert an unused office area to room. Problem 8-9 The Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Audience per advertisement Television Radio Newspaper 110,000 17,000 30,000 Cost per advertisement $2,500 $300 $500 Maximum media usage 10 23 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 40% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $20,500, how many commercial messages should be run on each medium to maximize total audience contact? No of commercial Advertisement Alternatives messages Television Radio Newspaper What is the allocation of the budget among the three media? Advertisement Alternatives Budget ($) Television Radio Newspaper $ $ $ What is the total audience reached? (b By how much would audience contact increase if an extra $100 were allocated to the ) promotional budget? Increase in audience coverage of approximately