Question: 1. (30 points) Consider the following linear program: + max 2 = -2.0 s.t. 201 2x2 2r2 - + + > 0, 2013 3 =

1. (30 points) Consider the following linear program: + max 2 = -2.0 s.t. 201 2x2 2r2 - + + > 0, 2013 3 = 23 > 13 2 4 -1 0 21 20, 32 (a) (5 points) Please write down the standard form of the above linear program (b) (5 points) When we use the big-M method to solve the above linear program, please introduce artificial variables and write down the standard form of big-M method. (c) 20 points) Please solve the original linear program using big-M simplex method. You might not need to fill all of the tableaus. (Please (i) write down the tableau, basic variables and nonbasic variables at each iteration, and (ii) answer the following questions: Can you find an optimal solution and the optimal value of Phase I linear program? If so, please write them down. If not, please explain.)

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