Question

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 maximize the profit for the airline. What is the maximum profit?

• A. $136000$
• B. $1360000$
• C. $13600$
• D. $1360$

Answer 1

The correct option is A $136000$

Let the airline sell $x$ tickets of executive class and $y$ tickets of economy class.
The mathematical formulation of the given problem is as follows.
Maximize $z=1000x+600y.......\left(1\right)$
subject to the constraints,
$x+y\le 200......\left(2\right)$
$x\ge 20..........\left(3\right)$
$y-4x\ge 0.......\left(4\right)$
$x,y\ge 0..........\left(5\right)$
The feasible region determined by the constraints is as shown
The corner points of the feasible region are $A(20,80),B(40,160)$ and $C(20,180)$
The values of $z$ at these corner points are as follows.
The maximum value of $z$ is $136000$ at $(40,160)$
Thus, $40$ tickets of executive class and $160$ tickets of economy class should be sold to maximize the profit and the maximum profit is Rs.$136000$.