Question

An aeroplane can carry a maximum of 250 passengers. A profit of ` 1,500 is made on

each executive class ticket and a profit of ` 1,000 is made on each economy class

ticket. The airline reserves at least 25 seats for executive class. However, at least 3

times as many passengers prefer to travel by economy class than by executive class.

Frame the Linear Programming Problem to determine how many tickets of each type

must be sold in order to maximize the profit for the airline.

Answer 1

Max Number of passengers = 250
Profit = 1,500 on an Executive class ticket.    
        = 1,000 on an economy class ticket.

Seats for executive class >= 25.
Number of passengers on Executive class = x
number of passengers on economy class = y

So given  x >= 25.  
                y >= 3 x.

   Given x + y = 250
              x = 250 - y
                  <= 250 - 3x
              4x <= 250
                x <= 62.5  or 62
                x <= 62.
                y >= 188.

Profit = P = x * 1,500 + 1,000 * y 
Maximize P.
    P = 1500 x + 1000 y = 1500 x + 1000 (250-x)
       = 500 x + 250,000
   
Max profit is when  :  x = 62
   P max = 500 * 62 + 250,000
              = 281,000.

Answer 2

Answer: yo

Step-by-step explanation: