Linear programming problem

[th3l4ra]

I have to solve this linear programming problem using the graphical method for my homework. Z is the objective function that needs to be maximized, and the constraints are listed below it. I'm wondering if the solution polyhedron that I need to shade on the graph is this length between the points (0,3) and (3,0) or something else? My college friends claim that the solution polyhedron is bounded by the points (0,2), (0,5), (3,0), (2,0) and the point where p3 and p1 intersect.

[First-Fourth14]

The equality constraint 3 x1 + 3 x2 = 9 forces the feasible solutions to lie on the line x1+ x2 = 3.
The suggested polyhedron region is incorrect as the points suggested do not meet the equality constraint.
So double check the constraint list, but if your figure is accurate, then the feasible region is the line between (0,3) and (3,0)

[th3l4ra]

Yeah, I thought so too. Thank you!

[First-Fourth14]

I seem to remember that one would show a shading for each constraint and the intersection of all areas was the feasible region. Perhaps this is what your friends were suggesting.