# Linear Programming Optimal Solution at (0,0)

I'm starting to learn about linear programming. On one of my HW questions I was able to write the LP, graph (shown below), and find the optimal solution (3,2) without a problem. When I checked my solution in the manual, I had everything correct expect the solution manual said that (0,0) is also in the feasible region and should be tested. Visually, (0,0) is not in the feasible region, so I must be missing something. This is the second question where (0,0) has been tested, even though it's not in the feasible region. I appreciate any insight you can provide.

Minimize $z=4p_1+p_2$

• Since you have both $p_1 \geq 3$ and $p_1 \geq 0$, I suspect that there is a typo in either the question or the solution, because you are completely right that $(0,0)$ is not in the feasible region. – Nigel Overmars Feb 2 '17 at 16:04