SYSTEMS OFINEQULAITIES LAB LINEAR PROGRAMMING

WHAT DAY IS IT? Graphing Systems of inequalities - How did I get here so quickly??

OBJECTIVES I can graph systems of inequalities and determine feasible regions. I can determine viable, possible, or correct solutions. I can locate maximum and minimum values which can occur under certain situations.

Example: The feasible area is shaded in yellow. The possible coordinates of the polygon are (0,8), (0,1) and (7,1). Test each coordinate to determine the maximum and minimum value of a function.

Function: f (x,y) = 2x + 3y Each vertex of the solution is tested. 2(0) + 3 (8) = = 24 2(0) + 3 (1) = = 3 2(7) + 3 ( 1) = = 17 Maximum Minimum

Example : Find a feasible region to represent this situation. Student Council is making colored armbands for the football team for an upcoming game. The schools' colors are blue and white. After meeting with students and teachers, the Following conditions were established: 1.The Council must make at least one orange armband but not more than 4 orange armbands since the orange armbands might be see as representing the opposing team. 2.The Council must make no more than 8 blue armbands. 3.Also, the number of orange armbands should not exceed the number of blue armbands.

Let x = orange armbands y = blue armbands y = blue armbands 1. x ≥ 1 and x ≤ 4 2. Y ≤ 8 3. x ≤ y The feasible region is shaded in yellow. The coordinates are ______________________

Example: Graph a system of two inequalities Test (0, -4)

1.

2. 3.

4. 5.