Question

An aeroplane can carry a maximum of 200 passengers. A profit of ₹1000 is made on each executive class ticket and a profit of  ₹600 is made on each economy class ticket. The airline reserves at least 20 seats for the 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 profit for the airline. What is the maximum profit ? Make an LPP and solve it graphically.

Answer 1

Let the executive class air tickets and economy class tickets sold be x and y.

Now, as the seating capacity of the aeroplane is 200, so x+y ≤ 200.

As 20 tickets for executive class are to be reserved, so we have x  ≥ 20.

And as the number of tickets of economy class should be at least 4 times that of executive class y  ≥ 4x.

Profit on sale of x tickets of 1st class and y tickets of economy class, Z = 1000x+ 600y.