How do I use linear programming to find maximum and minimum values?
The maximum and minimum values are found at the vertices.
In general, a linear programming graph will give you a polygon which contains all the possible combinations of the quantities involved.
The maximum and minimum values are found at the vertices, or if the vertices are not on whole numbers, then at the points INSIDE the polygon which are CLOSEST to the vertices.
Which vertex you will use will depend on the question asked.
It is a good idea to calculate an answer from several vertices to be sure of choosing the correct one.