Question

1. Transform the following linear program into a MAX and in standard form: (DO NOT SOLVE) min z = -2x, + 3x, st. *; -3x, + 2x, S3 - x + 2x 22 *; urs, x, 20, x, 20

Answer 1

Answer 1=

To convert the min problem to max, we have to multiply the objective function by -1

so the objective function will be

Max z= 2x1-3x2

Similarly, we will multiply al the constraints with -1 and change the inequality sign.

So the first constraint will be -x1+3x2-2x3$\geq$-3

as the objective function is Max so the inequality sign should be $\leqslant$ so we will again multiply the above equation with -1

x1-3x2+2x3$\leqslant$3

The second constraint will be x1-2x2$\leqslant$-2

So the constraints are

x1-3x2+2x3$\leqslant$3

x1-2x2$\leqslant$-2

TO convert it into standard form, we will add a slack variable

x1-3x2+2x3+S1=3

x1-2x2++S2=-2

and standard maximization LP will be as below

Max z= 2x1-3x2+0*S1+0*S2

x1-3x2+2x3+S1=3

x1-2x2++S2=-2