Question

While solving a linear programming problem(LPP) by simplex method, if all ratios of the right-hand side (bi)

to the coefficients of the entering variable become negative in a simplex iteration, then the LPP has?   

Select one:

a. Degeneracy

b. Infinite number of solution

c. No solution

d. Unbounded solution

Answer 1

Ans.option (d).Unbounded solution

Clearly ,unboundedness of a problem can occur only when the feasible solution is unbounded,which unfortunately,is something we cannot tell in advance of the solution attempt.We detect unboundedness when we encountered a pivot column that does not contain any positive entry.

The corresponding condition for unboundedness in a minimization problem is slightly different:We should look for a nonbasic column with a positive coefficient in R0 and with all other entries nonpositive.