The question goes...
Use the simplex method to solve the following linear programming problem. Maximise
subject to the constraints
This looks like a totally standard exercise in using the simplex method, so where are you having trouble with it?
Just to get you started, you should introduce "slack variables" u,v,w, to convert the inequalities into equations, namely
The objective equation is , which you write as .
Then you write down the simplex tableau, which is just the matrix of coefficients in these equations, and apply the simplex algorithm.
If it's any help to you, I wrote down a systematic description of the simplex algorithm a few years ago when teaching this stuff. You can find a copy of it here (pdf file).