Is it possible to recover the original objective function from a final simplex tableau?

Question

I have a problem that I couldn't find an answer here.

I would like to know if it is possible, given a final simplex tableau for a maximization problem, to recover the original coefficients of the objetive function. If is is, how to proceed?

More specifically, this is the tableau:

Thanks

Answer 1

Take variable $x_6$ for instance. Its reduced cost equals $\hat{c}_6= -2$, and by definition $$ \hat{c}_6 = c_6 - \pmatrix{c_1\\c_2\\c_3} \cdot \pmatrix{1/2\\-1\\5} = 0 - \frac{c_1}{2}-c_2+5c_3 $$ Write the same equations for the $2$ other slack variables and solve the set of equations for $c_1$, $c_2$, $c_3$.