max 3. [40 pts) Simplex Method and Duality. Solve the following LP problem z= 4x + 4x2 s.t. 2xy + 2x2 56 x1 + 2x2 > 2 xy + 3x2 2 x > 0,x2 > 0 (a) Write the LP standard form. 2 (b) Solve the LP using Big-M method or Two-Phase method and for each iteration, provide BV, NBV, current solution and objective value. (c) Sketch the feasible region of the original LP problem and highlight the optimal solu- tion obtained in Part (b). (d) What type of the original LP problem is? A. Unique optimal solution B. Multiple optimal solutions C. Unbounded (e) Write the dual of the original LP problem and then using complementary slackness equations, provide the optimal solution of the dual