Question: 4. [40 pts] Simplex Method and Duality. Solve the following LP problem min z = 2xy + 2x2 s.t. 3x1 + 2x2 15 2xy +

4. [40 pts] Simplex Method and Duality. Solve the
4. [40 pts] Simplex Method and Duality. Solve the following LP problem min z = 2xy + 2x2 s.t. 3x1 + 2x2 15 2xy + 4x2 10 X120,x220 (a) Solve the LP using Big M method or Two-Phase method and for each iteration, provide BV, NBV, current solution and objective value. (b) Sketch the feasible region of the original LP problem and highlight the optimal solu- tion obtained in Part (a). (c) What type of the original LP problem is? A. Unique optimal solution B. Multiple optimal solutions C. Unbounded (d) Write the dual of the original LP problem and write the corresponding complementary slackness equations (You needn't provide the dual optimal solution)

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