Question

1. All linear programs can be converted to symmetric form.?/

2. All linear programs can be converted to standard form.?

Answer 1

All linear program can be converted to standard form. Process is as follows-

(1) Negative variables can be converted to non negative by replacing it as -(-x) = - y where y=-x which is non negative.

(2) A constraint with negative RHS can be multiplied by -1 to get positive RHS.

(3) To make an inequalities equality we can add or subtract a slack variable.

(4) Unrestricted variables can be transformed to restricted variables by writing it into difference of two new non-negative variables.

Hence a Linear Program can always be converted into standard one.