Question: 4. [40 pts] Simplex Method and Duality. Solve the following LP problem min 2 = 2x1 + 2x2 s.t. 3x + 2x2 512 6x +

4. [40 pts] Simplex Method and Duality. Solve the following LP problem min 2 = 2x1 + 2x2 s.t. 3x + 2x2 512 6x + 4x2 2 15 2x + 4x2 20 X1 + 2x2 2 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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