Consider the linear program: max cx s.t. Ax c x 0. (1) We will assume that the above problem is feasible and bounded. (a) Write down the dual LP of the above LP (1). (b) Show that the feasible region of the primal LP and the dual LP is exactly the same, that is show that (a) if x is a feasible solution of the primal LP, it is also a solution of the dual LP, and (b) if y is a solution of the dual LP it is also a solution of the primal LP. [Note: This is a very rare property which is occurring due to the special-structure of the above LP. Typical LPs will never have this property.]