Please show us your work and let us know where you get stuck; we are not here to do out the entire problem for you.

To get you started, denote as . Declare your objective function .

Then your constraints become

The last two constraints can be ignored, as the Simplex Method itself requires all variables to be nonnegative. In other words, as you carry out your pivots correctly, the minimal ratio test will ensure that your variables say nonnegative.

For these three constraints, introduce slack variables and use that as your initial basis for a feasible tableau:

maximize

Your basis is currently [3,4,5] with an objective value of 0. Since both of them have positive reduced costs, choose one of as the entering variable k.

Can you take it from there? Check your answers by comparing the graphical and the Simplex method - they should agree with each other.