LP Graph Extreme Points & Feasible Region

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You really need to label your graph as that will help you out. You have sketched the lines but you haven't indicated which region you are interested in. (You need to indicate which side of the line actually gives solutions to the inequality).

Once you have done that if the problem has a solution the feasible region (the set of all points that satisfy all inequalities) will be clear as it will be the only region that where all the inequalities are met and this should be obvious from the diagram.

The extreme points are just the intersections of the lines you have drawn and if a solution exists to the LP problem then it will always lie on an extreme point.

So just use the equations of each line to find where they intersect (on the edge of the feasible region) and plug the intersection co-ordinates into whatever equation you want to max or min and see which is the solution.

Hope that helps.

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Yes.

Now:

1)sketch the feasible region.
2)determine the coordinates of the edges of the feasible reason using the equations of the lines.

3) see which is optimal solution

so theres only 3 extreme points?

wouldnt there be one at (9,45)?