08smid - 1 1. Convert the linear programming problem below...

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1 1. Convert the linear programming problem below to canonical form. minimize 3 x 1 - 2 x 3 subject to x 1 - 2 x 2 + x 3 = 1 x 1 + x 2 4 x 1 , x 2 0 , x 3 3 2. Given the linear programming problem minimize z = x 1 - x 2 subject to x 1 - 2 x 2 + 3 x 3 2 x 1 + 2 x 2 - x 3 1 x 1 , x 2 , x 3 0 (a) Show that x = (2 , 0 , 1) T is a feasible solution to the problem. (b) Show that p = ( - 1 , 2 , 1) T is a feasible direction at the feasible solution x = (2 , 0 , 1) T . (c) Determine the maximal step length α 0 such that x + α p remains feasible, where x and p are as in part (b). (d) Find all the feasible directions p = ( p 1 , p 2 , p 3 ) T at x = (2 , 0 , 1) T . 3. Given that the linear programming problem (1) maximize z = c T x subject to Ax b is feasible but unbounded, prove that if the linear programming problem (2) minimize z = c T x subject to Ax b is feasible, then it is also unbounded. (Hint: Write the duals.) 4. Given the linear programming problem minimize
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08smid - 1 1. Convert the linear programming problem below...

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