3) Eastjet Airlines is considering the purchase of new long-, medium-, and short

Question

3) Eastjet Airlines is considering the purchase of new long-, medium-, and short-range jet passenger airplanes. The purchase price would be $67 million for each long-range plane, $50 million for each medium-range plane, and $35 for each short-range plane. The board of directors has authourized a maximum commitment of $1.5 billion for these purchases. It is estimated that the net annual profit would be $4.2 million per long-range plane, $3 million per medium-range plane, and $2.3 million per short-range plane. It is predicted that enough trained pilots will be available to crew 30 new airplanes. 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 1 1/3 short-range plane, and each long-range plane is equivalent to 1 2/3 short-range planes in terms of their use of the maintenance facilities. Management wishes to know how many planes of each type should be purchased to maximize profit. Formulate and solve as Integer Program.

Explanation / Answer

Let [x] be number of short - range , [y] be number of midium - range and [z] be number of long -range aeroplanes

Then objective function is

Maximize [P=3x+5y+7z]

Subject to constraint s

[3x+5y+4z=15]

[4x+3y+2z=30]

[6x+5y+7z=80]

[x,y,zgeq0]

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