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I've hightlighted the section in the tableau I don't understand. Clearly the 28 comes from plugging in the 4 and 2 in the objective function but where do the other numbers in the row come from?

https://i.stack.imgur.com/d9p24.png

Any help is appreciated.

EDIT:

Oh, the objective function is $$z = 4{x_1} + 5{x_2}$$

callculus42
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MathGuy
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  • Have you answered your question by yourself ? Or what is your question ? In general it is hard to give an appropiate answer without knowing the previous tables. – callculus42 Nov 15 '15 at 16:34
  • No, I want to know where the entries I've highlighted come from. I haven't done any of the previous tables, that is literally the question. You're given the end result and you have to identify what these things are and be able to complete one which is incomplete. – MathGuy Nov 15 '15 at 16:50

1 Answers1

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You have identified right the objective function. Only the variables $x_1$ and $x_2$ ($\text{decision variables}$) are regarded to calculate $z_j$. And only the decision variables, which are in the basis are regarded. The $\text{slack variables}$ and $\text{artificial variables}$ are not regarded.

Let´s calculate $z_1$ (first column): $c_1\cdot a_{11}+c_2\cdot a_{21}=5\cdot 0+4\cdot 1=4$

And the calculation for $z_4$ (fourth column) is

$z_4=c_1\cdot a_{14}+c_2\cdot a_{24}=5\cdot \left(-\frac{1}{6} \right)+4\cdot \frac{1}{3}=-\frac{5}{6}+\frac{8}{6}=\frac{3}{6}=\frac{1}{2}$

callculus42
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