Answer:
Suppose the airline uses x planes of model 314 and y planes of model 535. \[\therefore \] Cost\[=\text{ }100000\,\,x+\text{ }150000\text{ }y\] Let Z denotes the profit. Then, \[Z=\text{ }100000x+\text{ }150000y\] and it is to be minimized. It is given that model 314 planes have 20 first class and 30 tourist class while model 535 have 20 first class and 60 tourist class seats. The group needs at least 160 first class seats and at least 300 tourist class seats. \[\therefore \] \[20x+20y\ge 160\] \[\Rightarrow \] \[x+y\ge 8\] Also, \[30x+60y\ge 300\] \[\Rightarrow \] \[x+2y\ge 10\] Finally, the number of planes cannot be negative. \[\therefore \] \[x\ge 0,\] \[y\ge 0\] Thus, the mathematical formulation of the given LPP is as follows Minimize \[Z=\text{ }100000x+\text{ }150000y\] Subject to constaints \[x+y\ge 8\] \[x+2y\ge 10\] and \[x,\,\,y\ge 0\]
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