Section 3.3
Linear Programming
Consider the following figure which is associated with a system of linear inequalities:
x
y
S
The set S is called a feasible set. Each point in S is a candidate for the solution of the
problem and is called a feasible solution.
The point(s) in S that optimizes (maximizes or minimizes) the objective function is called
the optimal solution.
Theorem 1 (in book) Linear Programming
If a linear programming problem has a solution, then it must occur at a vertex, or corner
point of the feasible set S associated with the problem. Furthermore, if the objective
function P is optimized at two adjacent vertices of S, then it is optimized at every point
on the line segment joining these vertices, in which case there are infinitely many
solutions to the problem.
The Method of Corners
1. Graph the feasible set (graph the system of constraints).
2. Find the coordinates of all corner points (vertices) of the feasible set.
3. Evaluate the objective function at each corner points.
4. Find the vertex that renders the objective function a maximum (minimum).
Section 3.3 – Linear Programming 1
