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I have this problem to be solved using the dual simplex method. I'm confused right now because there are a lot of different methods I've searched online. What are the steps in solving the problem using the dual simplex method, and what should I do about the equality constraints in converting it into its dual form? Is it correct to convert the constraints into less than or equal to? Any help is highly appreciated. Thanks!

Min $8x_1 +2x_2 $

subject to

$6x_1+2x_2=6$

$8x_1+6x_2 \geq 12$

$2x_1+4x_2\leq8$

$x_1,x_2 \geq 0$

Blake
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1 Answers1

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If you have $\min$-problem or a $\max$-problem and an equality, then the corresponding dual variable is unconstrained in sign (free). See the table here.

$$\textrm{primal:} \ \ 6x_1+2x_2=6 \quad (y_1)$$

$$\textrm{dual:} \ \ y_1 \textrm{ free}$$

callculus42
  • 30,550