(a) Recall that for any linear program, the three possible outcomes are: (i) LP is infeasible,...

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(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 ≥ 0, x₂ > 0. ii. minimize exp(-x) subject to x ≥ 1. (b) Show that the following LP is unbounded. maximize subject to X1 x1 X2 + x2 4x3 II X3 9x4 3x4 X3 X1, X2, x3, X4, X4 + + + +19 X5 7x5 X5 X5 4 3 ≥ 0. || || AI (LP1) (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 ≥ 0, x₂ > 0. ii. minimize exp(-x) subject to x ≥ 1. (b) Show that the following LP is unbounded. maximize subject to X1 x1 X2 + x2 4x3 II X3 9x4 3x4 X3 X1, X2, x3, X4, X4 + + + +19 X5 7x5 X5 X5 4 3 ≥ 0. || || AI (LP1)

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Part a Identifying NonLP Problems i Minimize x1 x2 subject to x1 0 x2 0 This is not an LP because the objective function and constraints are not linea... View the full answer