A local travel agent is planning a charter trip to a major sea resort. The eight days/seven nights package includes the fare for round-trip travel, surface transportation, board and lodging and selected tour options. The charter trip is restricted to 200 persons and experience indicates that there will not be any problem for getting 200 persons. The problem for the agent is to determine the number of Deluxe, standard, and economy tour packages to offer for this charter. These 3 plans differ according to seating and service for the flight, quality of accommodations, meal plans and tour options. The following table summarizes the estimated prices for the 3 packages and the corresponding expenses for the travel agent. The agent has hired an aircraft for the flat fee of 2,000,000 for the entire trip. Tour Map Deluxe Standard Economy Price 10,000 7,000 6,500 In planning the trip, the following should be considered. Prices and costs per tour package per person Hotel Costs 3,000 Meals and other expenses 4,750 2,200 1,900 2.500 2,200 a) At least 10% of the packages must be deluxe type. b) At least 35% but not more than 70% must be of the standard trip. c) At least 30 percent must be of the economy type. d) The maximum number of deluxe packages available in any aircraft is restricted to 60. e) The hotel desires that at least 120 of the tourists should be on the deluxe and standard packages together. The travel agent wishes to determine the number of packages to offer in each type so as to maximize the total profit. a) Formulate the above linear programming problem in terms of 2 decision variables, taking the fact the 200 packages will be sold. b) Find optimum solution using graphical method and I interpret your results.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 46P

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A local travel agent is planning a charter trip to a major sea resort. The eight days/seven nights package includes the fare for round-trip travel, surface transportation, board and lodging and selected tour options. The charter trip is restricted to 200 persons and experience indicates that there will not be any problem for getting 200 persons. The problem for the agent is to determine the number of Deluxe, standard, and economy tour packages to offer for this charter. These 3 plans differ according to seating and service for the flight, quality of accommodations, meal plans and tour options. The following table summarizes the estimated prices for the 3 packages and the corresponding expenses for the travel agent. The agent has hired an aircraft for the flat fee of 2,000,000 for the entire trip. Tour Map Deluxe Standard Economy Price 10,000 7,000 6,500 In planning the trip, the following should be considered. Prices and costs per tour package per person Hotel Costs 3,000 Meals and other expenses 4,750 2,200 1,900 2.500 2,200 a) At least 10% of the packages must be deluxe type. b) At least 35% but not more than 70% must be of the standard trip. c) At least 30 percent must be of the economy type. d) The maximum number of deluxe packages available in any aircraft is restricted to 60. e) The hotel desires that at least 120 of the tourists should be on the deluxe and standard packages together. The travel agent wishes to determine the number of packages to offer in each type so as to maximize the total profit. a) Formulate the above linear programming problem in terms of 2 decision variables, taking the fact the 200 packages will be sold. b) Find optimum solution using graphical method and I interpret your results.

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