Say we have been given a simplex tableau and let us assume that this isn't the first tableau (i.e. simplex has been run once or twice on it at this point). Can we convert this tableau back into the form of a linear program that will have the same optimal value as the one we've started with? I've attatched a tableau below so that we can discuss the same tableau.
Essentially, all the variables on the left-hand side are basic, and the value they take is the corresponding value on the right.