Write down the dual to the following LP: Choose nonnegative x₁, x₂, and x3 to minimize x₁ + x₂ + 2x3, subject to X₁ 23 2x2 + 2x3 24 x₂ + 3x3 ≥ 4. In the LP a) Show that x = (3,1,1) is feasible in the primal and y = (1,1/4,1/2) is feasible in the dual. b) What are the values of the two problems for these choices? c) Write down an optimal solution to the primal and an optimal solution to the dual.

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