Hi, I have the following problem (I have scanned and attached a file of what I have got so far...but I really don't know what I am doing)... It says:

Write down the following LP problem in standard form by introducing slack variables and . And also, use vertex enumeration to identify all vertices of the feasible region and, hence, determine an optimal solution to the problem.

maximise

subject to

So this is easy, I got:

maximise

subject to

So what I don't know is when a singular system is inconsistent (I've crossed through 2 rows, but I am not sure...), how you pick the values for the coordinates (there could be much more than 10 combinations and I don't know what I should look for)... and also, do I need to draw the LP problem to see which ones are feasible, or is there any other way I can work it out mathematically?

I would really appreciate it if you could give me a little explanation so that I can get this done before tomorrow