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  • 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

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