Question

An airline owns an aging fleet of Boeing 737 jet airplanes. It is considering a major purchase of upto 17 new boeing model 757 and 767 jets.the decision must take into account numerous cost and capability factors including the following
1)the airline can finance upto 1.6$ billion in purchases (2) each boeing 757 will cost 80$ million and each boeing 676$ will coat 110 million. (3)at least one-third of the planes purchased should be the longer range 757.(4)the annual maintenance budget is to be no more than $8 million.(5)the annual maintenance cost per757 is estimated to be 800000$ and it is 500000$.(6) each 757 can catry 125000 passenger per whereas each 676 can fly 81000 passengers annually. Formulate this an integer programming problem to maximize the annual passenger carrying capability. What categeory of integer programming problem is this.

Answer 1

This is maximisation case of LPP. The objective is to maximise the number of passengers Max P= 125000x+81000y, where x is the number of Boeing 757 and y is the number of 767 jets that should be purchased.

$\begin{cases} x+y \leqslant17, \\ 80\cdot 10^6x+110\cdot 10^6y \leqslant1600\cdot 10^6,\\ \frac{x}{x+y}\geqslant\frac 13,\\ 800000x+500000y\leqslant 8000000; \end{cases}$ $\begin{cases} x+y \leqslant17, \\ 8x+11y \leqslant160,\\ 2x\geqslant y,\\ 8x+5y\leqslant 80; \end{cases}$

where $x=5,~y=8$ and

Max $P=125000\cdot 5+81000\cdot 8=1273000.$