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Let the program linear :

$MaxZ=5x+4y+7z$

Subject to :

$3x+8y+2z≤40$

$9x+5y+7z≥35$

$7x+3y+3z≥51$

$x,y,z≥0$

Then given a basic solution $x^{*}=(4,2,6)$

Question is :

Find optimal (perfect ) solution of above program beginning from basic solution $x^{*}$

I don't have any ideas or hints

Wolfram alpha give $x^{*}=(0,0,20)$ and $z{*}=140$

But I don't know how I find it starte from a basic solution ??

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  • $\begingroup$ ummmm... You also had a problem on dual programs. Do you have a book about linear programming? When necessary, you introduce extra variables to change a system to a standardized form. One of my three books says to add a "slack" variable to change each $\leq$ constraint to an equality constraint. For each $\geq$ constraint, subtract one "excess" variable. However, you really should practice some linear programs in two variables, where you can draw a correct image of the feasible region. Also, this book does not mention the simplex algorithm until page 125... $\endgroup$ – Will Jagy Dec 4 '19 at 21:46

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