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If x is a decision variable of LPP and unrestricted in sign then this variable can be converted into x = x’ – x’’ so as to solve the LPP by simplex method, where:

If x is a decision variable of LPP and unrestricted in sign then this variable can be converted into x = x’ – x’’ so as to solve the LPP by simplex method, where: Correct Answer x’ and x’’ ≥ 0

Explanation:

  • Usually, in an LPP problem, it is assumed that the variables xj are restricted to non-negativity.
  • In many practical situations, however, one or more of the variables xj which can have either positive, negative, or zero value are called unrestricted variables.
  • Since, the use of the simplex method requires that all the decision variables must be non-negative at each iteration, therefore in order to convert an LPP problem involving unrestricted variables into an equivalent problem having only restricted variables, we have to express each of the unrestricted variables as the difference of two non-negative variables.
  • Suppose variable x be unrestricted in sign. We define two new variables say x' and x''such that 
  • x = x' - x'': x', x'' ≥  0

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