# tut6 - Forming an LP Dual Burr we shouldn't be fighting You...

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1 Forming an LP Dual Tim, the turkey I heard that today’s lecture is about forming the dual. Aaron Burr and Alexander Hamilton (not really) Hamilton, you’re going to die. Burr, we shouldn’t be fighting. You misunderstood me when I said we needed a dual.

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2 Forming Dual LPs in General Every linear program has a unique dual. The dual of the dual linear program is the original linear program. We will explain rules for taking the dual of a maximization problem. FIRST RULES 1. There is a dual variable for every constraint 2. The constraint matrix of the dual is the transpose of the constraint matrix of the primal. 3. The objective function and RHS are swapped. Ollie The first thing to remember is that every linear program has a dual, and there are simple rules for formulating the dual. Some of the rules are common to all linear programs. These are the first rules to learn.
3 A “standard” primal-dual pair The Primal LP Maximize z = 1 x 1 + 2 x 2 + 3 x 3 + 4 x 4 subject to 8 x 1 + 9 x 2 + 10 x 3 + 11 x 4 5 12 x 1 + 13 x 2 + 14 x 3 + 15 x 4 6 16 x 1 + 17 x 2 + 18 x 3 + 19 x 4 7 x 1 0, x 2 0, x 3 0, x 4 0 The Dual LP Minimize v = 5 y 1 + 6 y 2 + 7 y 3 subject to 8 y 1 + 12 y 2 + 16 y 3 1 9 y 1 + 13 y 2 + 17 y 3 2 10 y 1 + 14 y 2 + 18 y 3 3 11 y 1 + 15 y 2 + 19 y 3 4 y 1 0 y 2 0 y 3 0 y 1 y 2 y 3 Dual Variable

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4 What makes this pair of LPs the “standard” one? Ollie All linear programs have an objective, linear inequalities and inequalities, and variables. In the “standard” primal-dual pair (not to be confused with an LP in standard form), the max problem has constraints” and all variables are non-negative. The dual is a minimization problem with “ constraints” and non-negativity constraints. It’s important to remember this, as we shall soon see.
5 Nooz, the most trusted name in fox.

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tut6 - Forming an LP Dual Burr we shouldn't be fighting You...

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