question_answer 26)

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 th 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 ?  

Answer:

Let the number of executive class ticket = x       and the number of economy class tickets = 200             Atleast 20 seats of executive class are reserved.             Also atleast 4x seats of economy class are reserved               Therefore, above L.P.P. is given as       Maximize P = 1000 x + 600y subject to the constraints       x + y                  L1 : x + y = 200                    L2 : 4x ? y = 0                                            Here profit is maximum at F(40, 160)       40 tickets of executive class and 160 tickets of economy class to sold to get maximum profit and maximum profit is Rs.1,36,000.