Q. 44.0( 3 Votes )

Solve the following L.P.P. graphically :

Minimize

Subject to

Constraints



and [CBSE 2017]

Answer :

Minimize

Z = 5x + 10y


Subject to constraints


x + 2y ≤ 120


x + y ≥ 60


x – 2y ≥ 0


and x , y ≥ 0


Firstly, we draw the graph of the line x + 2y = 120



Put (0,0) in the inequality x + 2y ≤ 120, we get


0 + 2 × 0 ≤ 120


0 120 (which is true)


So, half plane is towards the origin.


Secondly, graph of the line x + y = 60



Put (0,0) in the inequality x + y ≥ 60, we get


0 + 0 ≥ 60


0 60 (which is false)


So, half plane is away from the origin.


Thirdly, draw the graph of line x – 2y = 0




On solving equations x – 2y = 0 and x + y = 60, we get B(40, 20)


and on solving equations x – 2y = 0 and x + 2y = 120, we get C(60, 30).


Feasible Region is ABCDA.



So, the minimum value of Z is 300 at the point (60, 0)


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