Question

An aeroplane can carry a maximum of 250 passengers, A profit of Rs. 1500 is made on each executive class ticket and a profit of Rs. 900 is made on each economy class ticket. The airline reserves at least 30 seats for executive class. However at least 4 times as many passengers prefer to travel by economy class than by executive class. Formulate LPP in order to maximize the profit For the airline.

Answer 1

Maximum number of passengers $=250$

Profit on executive class ticket $=Rs1500$

Profit on Economy class ticket $=Rs900$

Seats for executive class $\ge 30$

Numbers of passengers on Executive class $=x$

Numbers of passengers on economy class $=y$

So $x\ge 30$

$y\ge 4x$

Given $x+y=250$

$x=250-y$

$\le 250-4x$

$4x\le 250$

$x\le 50$ then $y\ge 200$

Profit $=1500x+900y$

Maximize $P$

$P=1500x+900y$

$=1500\times 50+900\times 200$

$=75000+180000$

$=255,000$