[Question 3] (The total marks available for this question is 20. The weighting of each subpart is indicated in %.) Consider the following linear program, where p is a parameter: Min 12x + 12x2 s.t. 3x +p x + x3 = 1, PX + 3x2 - 2x3 23, X1, X2, X3 20. (a) Suppose that p = 4. Write down the dual to the above program and solve it using the graphical method. [20%] (b) Still suppose that p = 4. Using complementary slackness conditions, solve the primal. [30%] (c) Now suppose that p = 3. By solving the dual with graphical method and using complementary slackness, show that the primal has multiple optimal solutions. Which of these optimal solutions (X, X, X3) has the largest component x? [50%]