Consumption and Real Estate
What are considered “corner points” in linear programming?
In precalc we are currently learning linear programming. However, my teacher isn’t very good at explaining things. I understand that corner points are solutions to the inequalities, but what I don’t understand is how you determine which set of solutions are corner points. Because aren’t there numerous solutions? So how do you determine which ones to use for finding the max and min of the objective function? Any help would be great. Thanks.
Hi,
If you determine all your inequalities and graph them, they will give you a shaded area for the entire system. Any point in the shaded region makes the inequalities true, but MINIMUM and MAXIMUM values always occur at a corner point along the outside of your shaded area.
So, find the intersection points of each side of your shaded figure. If it was in the shape of a triangle, there are 3 corner points on the triangle. A rectangle, parallelogram or trapezoid would have 4 corner points. Find all of their coordinates.
Then you will generally have a price formula or minimum cost formula with x and y variables in it. Plug your corner point values into this equation (which is not graphed) and find your minimum or maximum value that the problem wants.
I hope that helps!! Good luck with your math!!