Please wait...
1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number

022-62211530

Mon to Sat - 11 AM to 8 PM

Home / Doubts and Solutions/CBSE/Class 12 Science/Mathematics

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 July 2016, 7:21 PM
Answered by 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 Expert 31st July 2016, 9:21 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Report an issue
Previous Question
Next Question
Your answer has been posted successfully!

Free related questions

A function f: R -> R satisfies the equation f(x+y) = f(x).f(y) for all x'y E R, f (x) =/= 0.
 
Suppose that the function is differentiable at x=0 and f ' (0) = 2
 
Prove that f '(x) = 2 f ( x)
8th June 2016, 11:19 AM
Please find the roots for the equation 
 
 
 
8th June 2016, 4:29 PM
 
Ques:
17th June 2016, 10:14 AM
Ques:
17th June 2016, 12:17 PM
Ques:
17th June 2016, 11:04 AM
RELATED STUDY RESOURCES :
CBSE Class-12-science QUESTION ANSWERS

Chat with us on WhatsApp