Question

An aeroplane can carry a maximum of 200 passengers. A profit of Rs 500 is made on each executive class ticket out of which 20% will go to the welfare fund of the employees. Similarly a profit of Rs 400 is made on each economy ticket out of which 25% will go for the improvement of facilities provided to economy class passengers. In both cases, the remaining profit goes to the airline’s fund. The airline reserves at least 20 seats for executive class. However, at least four 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 net profit of the airline. Make the above as an LPP and solve graphically.

Answer 1

Let there be x tickets of executive class and y tickets of economy class be sold. Let Z be net profit of the airline.

Here, we have to maximise Z.

Now, Z = \(500x\times \frac{80}{1400}+400y\times \frac{75}{100}\)

Z = 400x + 300y  ........(i)

Subject to constraints :

x ≥ 20 ......(ii)

Also x + y ≤ 200 ........(iii)

x + 4x ≤ 200    [∵ y = 4x]

⇒ 5x ≤ 200

⇒ x ≤ 40 ....(iv)

Shaded region is feasible region having corner points A (20, 0), B (40,0) C (40, 160), D (20,180), E(0,200).

Now, value of Z is calculated at corner point as

Hence, 40 tickets of executive class and 160 tickets of economy class should be sold to maximise the net profit of the airlines.