Question: 1. (25 points) Consider the following problem: - 12 +212 52 - 211 +12 51 - 2x + 372 54 110,12 20 (a) (2 points)

1. (25 points) Consider the following problem: - 12 +212 52 - 211 +12 51 - 2x + 372 54 110,12 20 (a) (2 points) Sketch the feasible region. (b) (4 points) Show all basic feasible solutions. (c) (4 points) Suppose that the objective function is to maximize 21 + 432. What is the resulting solution obtained? (d) (5 points) What is the maximum number of iterations simplex method spends to find the optimal solution? Explain your answer otherwise, you will get 0 points even if your answer is correct)! (e) (5 points) Give an example of an objective function vector for which the problem is unbounded. Explain your answer (otherwise, you will get 0 points even if your answer is correct)! (1) (5 points) Give an example of an objective function vector for which the problem is bounded. Explain your answer (otherwise, you will get 0 points even if your answer is correct)

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