How many planes of each type should be purchased

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Reference no: EM133491146

Case: Southwestern Airlines is considering the purchase of new long-, medium-, and short-range jet passenger airplanes. The purchase price would be $201 million for each long-range plane, $150 million for each medium-range plane, and $105 million for each short-range plane. The passenger capacities for each long-, medium-, and short-range plane are 500, 200, and 50 respectively. Based on historical records, the airline company has to be able to transport 3000 passengers daily. The board of directors has authorized a maximum commitment of $4.5 billion for these purchases. In addition, the airline company must purchase at least three long-range jets, at least four mediumrange jets, and at least ten short-range jets in order to make the aircraft fleet complete. Regardless of which airplanes are purchased, air travel of all distances is expected to be sufficiently large that these planes would be utilized at essentially maximum capacity. It is estimated that the net annual profit (after capital recovery costs are subtracted) would be $12.6 million per long-range plane, $9 million per medium-range plane, and $6.9 million per short-range plane. There are 65 trained pilots available to operate these new airplanes. For each long-range jet, 5 pilots are needed, 3 are needed for each medium-range jet, and 2 are needed for each short-range jet. If only short-range planes were purchased, the maintenance facilities would be able to handle 40 new planes. However, each medium-range plane is equivalent to 4 3 short-range planes, and each long-range plane is equivalent to 5 3 short-range planes in terms of their use of the maintenance facilities.

Question 1: Formulate the algebraic LP model whose objective is to know how many planes of each type should be purchased to maximize profit. Define the decision variables, objective function, and constraints.

Question 2: Formulate this same linear programming problem on a spreadsheet and SOLVE using Excel Solver (Provide the corresponding "Excel Spreadsheet" and the "Answer Report"). Include "managerial statements" that communicate the results of the analyses. (i.e., describe verbally the results).

Reference no: EM133491146

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