Consider the LP problem max x1 x2 4x3 subject to 2x1 x2

Consider the LP problem max x1 - x2 - 4x3 subject to 2x1 - x2 + x3 LE -1 3x1 + 5x2 - 5x3 LE 6 x1,x2,x3 GE 0 Let c2 be the coefficient for x2 in the objective function. Determine all the possible values of c2,, such that optimalityismaintained ?

Solution

Entering =X2, Departing =A1, Key Element = 1

R1 (new) =R1(old)

R2 (new) =R2 (old) 5R1 (new)

Since all CjZj0,

Optimum Solution is arrived with value of variables as :
X1=0

X2=1

X3=0

Maximise Z=1

MAX Z= 1 X1 1 X2 4 X3

Subject to constraints

2 X1+ 1 X2+ 1 X3 1 3 X1+ 5 X2+ 5 X3 6

and X1,X2,X30