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# a9 - C O350 L INEAR O PTIMIZATION HW 9 Due Date Friday July...

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CO350 L INEAR O PTIMIZATION - HW 9 Due Date: Friday July 13th, at 2pm, in the drop box outside the Tutorial Center. Recall, late assignments will not be graded. Exercise 1. Consider the following linear program (P) max { c T x : Ax = b, x 0 } where A = " 1 1 2 0 2 2 3 3 1 2 # b = " 3 7 # c = 5 8 4 2 3 (1) Formulate the auxiliary problem (P’). (2) Solve (P’) using the revised simplex. (3) Solve (P) using the revised simplex starting from the solution obtained for (P’). Exercise 2. Let B := { x ∈ < n : x T x 1 } . Recall, k x k = x T x corresponds to the length of x . Thus B is the set of points in an n -dimensional space which are at distance at most 1 from the origin, i.e. B is the n -dimensional unit sphere. It is intuitively clear that a sphere is convex. In this exercise, you are asked to give an algebraic proof (using the definition of convexity seen in class) of the fact that B is convex.

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a9 - C O350 L INEAR O PTIMIZATION HW 9 Due Date Friday July...

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