# MAT 114 Lecture Notes - Lecture 8: Linear Programming, Lincoln Near-Earth Asteroid Research, Feasible Region

## Document Summary

A linear programing problem in two unknowns x and y is one in which we are able to find the maximum or minimum value of a linear expression t by. Ix called the objective function subject to a number of linear constraints of the form. Solution the set of all points lay 1 satisfying all the constraints is the feasible region for the problem an optimal. If an lp problem has optimal then at least one of those solutions occurs at a corner point of the feasible region. Linear programming problems with bounded nonempty feasible regions alwab have optimal solutions. 1 graph the feasible region and check that it is bounded. 2 compute the coordinates of the corner points. 3 substitute the coordinates of the corner points into the objective function to see which gives the maximum or minimum 1 value of the objective function. 4 any such corner point is an optimal solution.