An aeroplane can carry a maximum of 200 passengers. A profit of Rs 400 is made on each first class ticket and a profit of Rs 300 is made on each economy class ticket. The airline reserves at least 20 seats for first class. However, at least 4 times as many passengers prefer to travel by economy class to by the first class. Determine how many each type of ticket must be sold in order to maximum the profit for the airline. What is maximum profit?

Asked by Topperlearning User | 31st Jul, 2016, 07:21: PM

Expert Answer:

Let x and y be the numbers of first class tickets and economy class tickets respectively we have the following LPP

 


Maximum 400x + 300y
          st x + y  200
          x  20
          y  4x
          x  0, y  0 

 

Let us draw the graph of the above LPP

 

 


 

Thus, the feasible region is ABC and the corner points are A(20,180), B(40,160) and C(20,80)

 

The value of the objective function at the corner points are:

 

table row cell C o r n e r space p o i n t end cell cell V a l u e space o f space Z equals 400 x plus 300 y end cell row cell A left parenthesis 20 comma 180 right parenthesis end cell 62000 row cell B left parenthesis 40 comma 160 right parenthesis end cell 64000 row cell C left parenthesis 20 comma 80 right parenthesis end cell 32000 end table

 

The maximum of the objective function is 64000 and it attains at A(40,160).

 

That is 40 first class tickets and 160 economy class tickets must be sold to get the maximum profit.

 


 


 


 

 

 

Answered by  | 31st Jul, 2016, 09:21: PM