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Write down the dual of the linear programming problem:

Max. : $2x + 3y$

such that

$x + 2y = 3$

$2x + y ≥ 4$

$x + y ≤ 5$

$x ≥ 0 , y ≥ 0.$

My attempt : Min $ 3w_1 + 4w_2$ such that

$w_1 + 2w_3 +w_3 \ge 2$

$2w_1 +w_2 +w_3 \ge 3$

$w_1 \ge 0 , w_2 \ge 0$

Is its true ?

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jasmine
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1 Answers1

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Many things are right, but there are some mistakes. Especially the variable $w_3$ must be at the objective function. I´ve used the table below to obtain the dual program.

$\texttt{min} \ \ 3w_1 + 4w_2+5w_3$ such that

$w_1 + 2w_3 +w_3 \ge 2$

$2w_1 +w_2 +w_3 \ge 3$

$w_2\leq 0, w_3\geq 0$

enter image description here

callculus42
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