1. Consider the following LPP Without using artificial variable(s), solve the given LPP (do not solve the dual problem). Write the dual of the above problem.
2. Consider the following LP
Using M-method solve the above LP. Does the problem has alternative optimal solution? If so, find all the alternative optimal solutions.Write the dual of the above problem. Also, write the optimal solution of the dual problem (from the optimal table of part
(a)).What can you conclude regarding the relationship of solution of primal and dual problems?
3. The following is an optimal LP tableau:
The variables,andare slacks in the original problem. Using matrix manipulations, reconstruct the original LP, and then compute the optimum objective value. Also, compute the optimum objective value by using dual objective function.