Please show all work in solving all parts so that I can better understand. Thank you!

Consider the following problem: Maximize Z=x13x2+2x3, Subject to: 2x1+2xx22x3=0. (i) Set up the dual model. (ii) Solve the dual model graphically and identify the optimal solution. (ii) Use the complementary slackness theorem to identify the optimal primal solution. Validate the optimal primal solution. (iv) Identify a primal feasible solution and a dual feasible solution by inspection and validate the weak duality theorem. Consider the following problem: Maximize Z=x13x2+2x3, Subject to: 2x1+2xx22x3=0. (i) Set up the dual model. (ii) Solve the dual model graphically and identify the optimal solution. (ii) Use the complementary slackness theorem to identify the optimal primal solution. Validate the optimal primal solution. (iv) Identify a primal feasible solution and a dual feasible solution by inspection and validate the weak duality theorem