Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 51

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 51

Answers (1)

Answer:

Max Profit = Rs.1, 36,000 when 40 first class tickets and 160 economy class tickets are sold.

Hint:

Form Linear Equation and solve graphically.

Given:

An aero plane can carry a maximum of 200 passengers. A profit of Rs.1000 is made on each first class ticket and a profit of Rs.600 is made on each economy class ticket. The airline reserves at least 20 seats of first class. However, at least 4 times as many passengers prefer to travel by economy class to the first class.

Solution:

Let required number of first class and economy class tickets be x and y respectively.

Each ticket of first class and economy class make profit of Rs.1000 and Rs.600 respectively.

So, x ticket of first class and y tickets of economy class make profit of Rs.1000x and Rs.600y respectively.

Let total profit be Z=1000x+600y

Given, aero plane can carry a minimum of 200 passengers, so x+y \leq 200

Given, airline reserves at least 20 seats for first class, so x \geq 20

Also, at least 4 times as many passengers prefer to travel by economy class to the first class, so

                y \geq 4 x

Hence the mathematical formulation of the LPP is

Max Z = 1000x+600y

Subject to constraints

                \begin{aligned} &x+y \leq 200 \\ & \end{aligned}        

                x \geq 20 \text { And } y \geq 4 x \\

x, y \geq 0 {Seats in both the classes cannot be 0}

 

The feasible region determined by the given constraints can be diagrammatically represented as.

 

The corner points are A(20,80), B(40,160), C(20,180)

 

The values of Z at these corner as follows

Corner Points

z=1000x+600y

O

0

A

68000

B

136000(maximum)

C

128000

The maximum value of Z is attained at B(40,160).

Thus, the max profit is Rs.136000 obtained when 40 first class tickets and 160 economy class tickets sold.

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question