Question

Solve by big M method Max Z=-2x-y Subject to constraints 3x+y=3 4x+3y>=6 X+2y=0​

Answer 1

Answer:

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Answer 2

given,

(A)

Z=-2x-y.(1)

Subject to constraints

3x+y=3

4x+3y>=6

X+2y=0​

covert these inequalities into equations

3x+y=3.(2)

4x+3y=6(3)

X+2y=0​.(4)

From (2) we get

x=0

y=3

and

y=0

x=1

so, the point (0,3) and (1,0) lie on the line given in(2)

From (3) we get the points

(0,2) and (1.5,0)

From(4) we get the points

(0,0) and (0,0)

(B)

line (2) and (3)  intersect at (0.5 , 1) and other corner point of the region are (0,2),(1.5,0) and (0,0).

(C)

To find the maximum value of z

corner points       z= -2x-y

(0,0)                         0

(1.5,0)                      -3

(0,2)                        -2

(0.5, 1)                     -2

Thus , Z is maximum at (0.5,1 ) and its maximum value is -2.