linear programming problem work out problem Minimize Z3X12X2

linear programming problem, work out problem

Minimize

Z=3X1+2X2 + 4X3

ST

X2+X3 >=10

2X1+X2+X3 <=60

2X1+3X2 +5X3=30

X1, X2, X3 >=0

Solution

you can follow the example given below

The given problem is minimization type and all the constraint should be >= type. In the
given problem third constraint is <= type so we must convert constraint to >= type by
multiply both side of the constraint by -1, we get
-7x1 +2 x3 +x3 > = - 10
Then given the problem can be written restated
Min Z = 3x1 -2x2 + 4x3
STC
3x1 +5x2+4 x3 >=7
6x1 +x2+ 3x3 > = 4
-7x1 +2 x2 +x3 > = -10
x1 -2x2+5 x3 >= 3
4x1 +7x2-2 x3 >= 2
x1, x2, x3 >= 0
Then dual of the given problem is as follows and the dual variables are y1 ,y2 ,y3,y4 y4
Max Z = 7y1 +4y2 -10y3+3y4 +2y5
STC
3 y1 +6y2 -7y3+y4+4y4 >= 3
5y1 +y2 +2y3-2y4 +7y4 > = -2
4y1 +3y2 +y3+5y4 -2y4 > = 4
y1 ,y2 ,y3,y4 ,y5 >= 0