1. ALGEBRA II HONORS/GIFTED SECTION 3-4 : LINEAR PROGRAMMING@
SECTION 3-4 : LINEAR PROGRAMMING
ALGEBRA II HONORS/GIFTED - SECTION 3-4 (Linear Programming)

2. Graph the system of inequalities on one coordinate system (but off to the side!).
x + y < 6
2x + y < 10
x > 0
y > 0
ALGEBRA II HONORS/GIFTED - SECTION 3-4 (Linear Programming)

3. What are the constraints for this problem?
LINEAR PROGRAMMING : A method for finding minimum or maximum values for some quantity given a set of constraints.
What are the constraints for this problem?
The four inequalities.
FEASIBLE REGION : The points that satisfy all of the constraints.
ALGEBRA II HONORS/GIFTED - SECTION 3-4 (Linear Programming)

4. Where is the feasible region for our graph? Note it on the graph.
OBJECTIVE FUNCTION : The quantity you are trying to minimize or maximize.
In our case, the objective function is P = 4x + y, which we are trying to maximize.
ALGEBRA II HONORS/GIFTED - SECTION 3-4 (Linear Programming)

5. What are the vertices for our problem?
In order to find the minimum or maximum, we need to look at the vertices of the feasible region. The vertices occur at the corners of the feasible region.
What are the vertices for our problem?
(5, 0), (4, 2), (0, 6), (0,0)
How do we find the maximum?
Test each of the points.
ALGEBRA II HONORS/GIFTED - SECTION 3-4 (Linear Programming)

6. So, the point (5, 0) generates a maximum.
Determine whether the following points satisfy the system of inequalities. List all that apply.
(2, 1) (1, 4)
(5, 2) (1, 5)
(4, 0.5) (3, 2)
(2, 1), (3, 2), (1, 4), (4, 0.5), (1, 5)
ALGEBRA II HONORS/GIFTED - SECTION 3-4 (Linear Programming)

7. ALGEBRA II HONORS/GIFTED - SECTION 3-4 (Linear Programming)