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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 22

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 22

Answers (1)

Answer:

Max Profit = Rs.116000 when 20 first class tickets and 180 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.400 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.400 and Rs.600 respectively.

So, x ticket of first class and y tickets of economy class make profit of Rs.400x and Rs.600y respectively.

Let total profit be Z=400x+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=400x+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}

Region represented by  x+y \leq 200 : the line x + y = 200 meets the axes at A(200,0), B(0,200). Region containing origin represents x+y \leq 200 as (0,0) satisfies x+y \leq 200

Region represented by x \geq 20 : line x=20 passes through (20,0) and is parallel to y-axis. The region to the right of the line x=20 will satisfy the in equation x \geq 20

Region represented by y \geq 4 x : line y=4x passes through (0,). The region above the line y=4x will satisfy the in equation y \geq 4 x

Region x, y \geq 0   : it represents the first quadrant.

                                                                                                Scale: On y-axis, 1 big Division=100 units

                                                                                                            On x-axis, 1 big Division=50 units

                 

 

The corner points are C(20,80), D(40,160), E(20,180)

The values of Z at these corner as follows

Corner Points

z=400x+600y

O

0

C

56000

D

112000

E

116000

The maximum value of Z is attained at E(20,180).

Thus, the max profit is Rs.116000 obtained when 20 first class tickets and 180 economy class tickets sold.

Posted by

infoexpert27

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