Suppose the variable x₁ can assume any real value. Show that the following substitution using nonnegative variables x₂ and x₃ permits x₁ to assume any real value.

Thus, if a computer code allows only nonnegative variables, the substitution allows for solving the linear program in the variables x₂ and x₃ and then recovering the value of the variable x₁.

Transcribed Image Text:

and X1 = X2-X3, X 0 where x is unconstrained and X3 0