Question: Q1 [10 marks] (a) Recall that for any linear program, the three possible outcomes are: (i) LP is infeasible, (ii) LP is unbounded, or (iii)

Q1 [10 marks] (a) Recall that for any linear program, the three possible outcomes are: (i) LP is infeasible, (ii) LP is unbounded, or (iii) LP has an optimal solution. For each of the following problems explain why it is not an LP problem and show that it has no optimal solution, is not infeasible and is not unbounded. i. minimize x1 + x2 subject to x 2 0, x2 > 0. ii. minimize exp (-x) subject to x 2 1. (b) Show that the following LP is unbounded. + 705 - 2 2 + 4x3 - 4 maximize 1 (LP1) subject to + 9x4 + X1 3x4 - IV II II 2 2 3

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