# Find optimal solution from given a basic solution?

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 ??

• 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... – Will Jagy Dec 4 '19 at 21:46