Linear Programming problem Use BigM method to solve the foll

Linear Programming problem

Use Big-M method to solve the following LP. Also solve the LP using graphical method and verify your solution. max z = x_1 + x_2 s.t. 2x_1 + x_2 3 3x_1 + x_2 3.5 x_1 + x_2 1 x_1, x_2 0

Solution

SOL)

Entering =X1, Departing =S2, Key Element = 1

R3 (new) =R3(old)

R1 (new) =R1 (old) 2R3 (new)

R2 (new) =R2 (old) 3R3 (new)

Since all CjZj0,

Optimum Solution is arrived with value of variables as :
X1=1

X2=0

Maximise Z=1

MAX Z= 1 X1+ 1 X2

Subject to constraints

2 X1+ 1 X2 3 3 X1+ 1 X2 3.5 1 X1+ 1 X2 1

and X1,X20