Please answer the question in short answer paragraph form 1

Please answer the question in short answer (paragraph) form.

(1) During the steps of Simplex algorithm to solve a linear program in maximization form, under which condition this problem is unbounded?

Under the duality theorems, what is the solution case for its dual problem?

Solution

Solution: The LPP is unbounded when we cannot find the minimum ratio i.e, if all the elements of key column are less than equal to zero. In that case we cannot proceed further and get a unbounded solution.

In simplex algorithm, minimum ratio = RHS/ corresponding element of key column, where all the elements of key column should be strictly positive.

If primal problem has an unbounded solution, then by duality theorem the dual of that problem is infeasible.