A local travel agent is planning a charter trip to a major sea port. The eight day and seven night package includes the fare for round trip, surface transportation, board and lodging and selected tour options. The charter trip is restricted to 200 persons and past experience indicates that there will not be any problem for getting 200 clients. The problem for the travel agent is to determine the number of Deluxe, Standard and Economy tour packages to offer for this charter. These three plans differ according to seating and service for the flight, quality of accommodations, meal plans and tour options. The following table summarises the estimated prices for the three packages and the corresponding expenses for the travel agent. The travel agent has hired an aircraft for the flat fee of Rs 2,00,000 for the entire trip.

In planning the trip, the following considerations must be taken into account:

(i) At least 10% of the packages 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 maximise the total profit.

(a) Formulate this as a linear programming problem.

(b) Restate the above LPP in terms of two decision variables, taking advantage of the fact that 200 packages will be sold.

(c) Find the optimal solution using graphical method for the restated problem and interpret your results.

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Tour Plan Prices and Costs for Tour Packages per Person Hotel Costs Meal and Other Expenses 4,750 Price Deluxe 10,000 3,000 Standard 7,000 2,200 2,500 Economy 6,500 1,900 2,200