An aeroplane can carry a maximum of 200 passengers. A profit of Rs.1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit ?

.: Let ‘x’ passengers travel by Executive class and ‘y’ passengers travel by Economy class.

Then, the LPP problem is as below :

Maximize : $Z = 1000x + 600y$ ...(1)

Subject to constraints : $x + y \le 200$ ...(2)
$x \ge 20$ ...(3)

$y \ge 4x$ ...(4)

and $x,y \ge 0$ ...(5)

${l_1}:x + y = 200;{l_2}:x = 20;{l_3}:y = 4x$

Let us graph the inequalities (2) to (5).

The feasible region (shaded) determined by the constraints (2) to(5) is

shown in the graph and note that it is bounded.

Let us evaluate the corner points at E(20, 80), F(40, 160), G(20, 180)

From the table, we find that Z is maximum at the point F(40, 160).

Hence, the maximum profit is Rs. 136000 when

40 passengers travel in Executive class and 160 passengers travel in Economy class.