In Linear programming, you want to optimize stuff. For example; minimize the costs and maximize the profit. We have a series of constraints, in my case on either 2 or 3 variables. You can draw them in a coordinate system and you'll get a feasible region. If I understood correctly; one of the vertexes of feasible region is the optimization.
- How do you know which vertex is the solution to your problem? Also, how do you get the exact coordinates of the vertexes. Consider this example:
$$a \geq 0$$
$$ u \geq 0$$
$$ a + u \leq 20$$
$$5a + 8u \leq 120$$
If I draw this, I get a simple polygon. How do I find the coordinates of the vertexes and more importantly, how do I know that a certain vertex is the one I'm looking for? Let's say in this case I want to minimize, and maximize (just to help my understand both with 1 example).