2. (5pts) For each below description of a pair of primal and dual LPs, please determine if such a relation is possible and, if possible, construct a pair of LPs that match the description. Your sample LPs should have no more than two variables and two constraints each. Both the primal and dual have an optimal objective value of 0. . Both the primal and dual have no feasible solutions. . Both the primal and dual have feasible solutions and an unbounded objective. The primal has feasible solutions and an unbounded objective, while the dual has no feasible solutions. . The primal has feasible solutions and an unbounded objective, while the dual has an optimal objective value of 0. 3. (4pts) Consider the Wyndor LP model presented in section 4.1 of the class notes. Suppose the processing time for Product 2 in Plant 3 is doubled, so that each batch of Product 2 requires 4 hours of production time in Plant 3. Is the optimal basis from the original version of the problem still optimal with this change? Justify your answer.