Consider the linear program 2x2 + x3 max -21 x2 X1 + X2-3 2x1 + x2...

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Consider the linear program 2x2 + x3 max -21 x2 X1 + X2-3 2x1 + x2 3x1 - x2 - 2x3 x1 x2 > -1 IV IV IV IVIA IV IA IV ≤2 224 2 X3 20 -5 Consider the point r* = (1,2,1). (a) Show that r* is an extreme point. (b) Write down all sets of defining constraints at r*. (c) Is r* a degenerate extreme point? Justify your answer. (A) (B) (C) (D) (E) (F) (H) (d) Show that r* is an extreme optimal solution of the linear program. (e) Show that r* is the unique optimum. (f) Determine which set(s) from (b) provide a proof of optimality for r*. Justify your answer. Consider the linear program 2x2 + x3 max -21 x2 X1 + X2-3 2x1 + x2 3x1 - x2 - 2x3 x1 x2 > -1 IV IV IV IVIA IV IA IV ≤2 224 2 X3 20 -5 Consider the point r* = (1,2,1). (a) Show that r* is an extreme point. (b) Write down all sets of defining constraints at r*. (c) Is r* a degenerate extreme point? Justify your answer. (A) (B) (C) (D) (E) (F) (H) (d) Show that r* is an extreme optimal solution of the linear program. (e) Show that r* is the unique optimum. (f) Determine which set(s) from (b) provide a proof of optimality for r*. Justify your answer.

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