# Reconstructing an optimal Simplex tableau from an optimal solution

I have here a bounded LP with infinite optimal solutions:

max    60 x1 + 100 x2 +  80 x3
s.t.  144 x1 + 192 x2 + 240 x3 <= 120,000
100 x1 + 150 x2 + 120 x3 <= 60,000
x1 +     x2 +     x3 <= 500
x >= 0


My Operations Research teacher has hinted that you can reconstruct an entire optimal tableau from the optimal solution and the initial LP. I can easily find the Basis and reconstruct the entirety of the tableau, except for the objective row. What I've done now was a really roundabout way of using MATLAB to find an optimal solution (doing this LP by hand is messy, and we've already had plenty of simplex method homework), finding B^-1 and multiplying through the tableau, which revealed a simpler optimal solution, and then running the simplex method again by hand, but rigging my choices of entering and leaving variables to get the basis I want.

There's a simpler way, yes?

-