Write the following LP in canonical inequality form ie formu

Write the following LP in canonical inequality form (i.e., formulate an equivalent LP that has canonical inequality form):

min 2x1 + x2 + x3

s.t. 4x1 + 3x2 + 2x3 3

2x1 x2 3x3 1

x1 + x2 + x3 = 1

x1 0

x2 7

0 x3 3.

Solution

we have to cange the given inequality constraintsin lpp into canoniaclal form so

1. objective should be Max.

2. inequality should be <= constraints

3. variables must be non negative

give,

w=min (-2x1+x2+x3)

st 4x1+3x2+2x3<=3

2x1-x2-3x3>=1

x1+x2+x3=1

x1>=1

x2>=-1

<=x3<=3

Max(z=-w= 2x1-x2-x3)

st

4x1+3x2+2x3<=3

-2x1+x2+3x3<=-1      {negative of second constraints}

x1+x2+x3<=1             { break in two parts <= and >= }

-x1-x2-x3<=-1

-x1<=0

-x2<=7

-x3<=0              { break into two parts x3>=0 ,x3<=0 }

x3<=3