Example 1.7 A local travel agent I planning a character trip to a major sea port. The eight day seven-night package includes the far for round-trip travel, surface transportation, board and lodging and selected tour options. The character trip is restricted to 200 persons and past experience indicates that there will not be any problem for getting 200 persons. The problem for the travel agent is to determine the number of Deluxe, Standard and Economy tour packages to offer for this character. These three plans each differ according to seating and service for the flight, quality of accommodation, meal plans and tour options. The following table summarizes the estimated prices for the three packages and the corresponding expenses for the travel agent. The travel agent has hired an air craft for the flat fee of Rs. 2,00,000 for the entire trip. Prices and costs for tour package per person Tour Plan Price Hotel Costs Meal and other expenses Deluxe 10000 4750 3000 Standard 7000 2500 2200 Economy 6500 2200 1900 NJU 1.28 In planning the trip, the following considerations must be taken into account (1) At least 30% of the package must be of the deluxe type. (ii) At least 35% but not more than 70% must be of the Standard type. (iii) At least 30% must be of the Economy type. (iv) The maximum number of deluxe packages available in any aircraft is restricted to 60 (v) The hotel desires that at least 120 of the tourists should be on the Deluxe and Standard packages taken together. The travel agent wishes to determine the number of packages to offer in each type so as to maximize the total profit. 1. Formulate this as Linear programming problem. 2. Restate the above Linear Programming Problem in terms of two decision variables, taking advantage of the fact that 200 packages will be sold. 3. Find the optimal solution using graphical method for the restated problem and interpret your results. A.IT Na