Linear Programming Chapter 3 Lesson 4

Vocabulary Constraints- Conditions given to variables, often expressed as linear inequalities. Feasible Region- The intersection of the graphs in a system of constraints. Bounded-A region is bounded when the graph of a system of constraints is a polygonal region. Vertex- Any of the points of intersection of the graphs of the constraints that determine a feasible region. Unbounded- A system of inequalities that forms a region that is open. Linear Programming- The process of finding the maximum or minimum values of a function for a region defined by inequalities.

Steps to Solving Homework Problems 1. Graph each system of inequalities 2. Name the coordinates of the vertices of the feasible region 3. Find the maximum and minimum values of the given function for this region

1) Graph the system of inequalities 2) Find the Vertices Same process as last section y ≥ 2 x ≥ 1 x + 2y ≤ 9

3)Find the maximum and minimum values of the given function for this region FINALLY a part that isn’t a repeat of last section. Using the coordinates of the vertices and the given equation Plug the values for x and y into the equation and solve Of all the outputs, the highest is the maximum, and the lowest is the minimum

Example Pg 141 #1 (x,y)2x-3yF(x,y)

Example #3 (x,y)x-2yF(x,y)

Example (x,y)x+yF(x,y) #15

Example (x,y)3x-2yF(x,y) #17

Example (x,y)-x+3yF(x,y) #5 on worksheet

Word Problems on Back

Homework Worksheet 3-4