Week 17, Day 3

As we continued our review, Harrison presented on lesson 7.6: Linear Programming. In this lesson, we learned how to perform linear programming. A 2D linear programming problem consists of a linear objective function and a system of linear inequalities called constraints. The objective function gives the quantity that is to be maximized or minimized, and the constraints determine the set of feasible solutions.

The following are steps to solving a linear programming problem:

1) Sketch the region corresponding to the system of constraints.

2) Find the vertices of the region.

3) Test the objective function, z = ax + by, at each of the vertices and select the values of the variables that optimize the objective function. For a bounded region, both a maximum and minimum will exist. For an unbound region, if an optimized solution exists, it will occur at a vertex.