Question: Diamond Tours and Travels is planning to charter a trip to a hill resort. The cost of tour package includes the fare for round trip, surface transportation, food, stay and site seeing. The trip is restricted to 200 persons and as per past experience there will be no difficulty in getting 200 persons for the trip. The problem of the tour operator is to determine the best number of Deluxe, Standard and Economy tour packages for this charter tour. The three plans differ according to the facilities offered to the customers in terms of quality of accommodation, food plan and other tour options. The following table summarizes the estimated pieces and corresponding expenses for the travel agent.

Price and cost for tour package per person

- In deciding the number of persons in each category the following constraints must be taken into account.

- At least 10 % packages must be of the deluxe type.

- At least 35 % but not more than 70 % must be of standard type.

- At least 30 % must be of economy type.

- The maximum number of seats for the deluxe package in the air craft is restricted to 60.

- The hotel requires that at least 120 persons should be on the deluxe and standard packages put together.

- The travel agent wishes to determine the number of packages to offer in each category so as to maximize his profit.

- Formulate the above as linear programming problem in three variables.

- Restate the problem in terms of two variables by discarding the economy type.

- Solve the restated problem graphically to determine the gross contribution.

- If the cost of hiring aircraft is Rs. 200000 what is the highest possible profit