More on systems of inequalities
Shade the region defined by the following sets of inequalities:
2x + y 15
x + 3y 20
x + 2y 10
2x + 3y 18
A: -2x + y -4
B: x + 3y 9
C: -2x + y 3
-4x + 2y 2
4x - 2y 6
6x - 3y 9
2x 4y 13
4x 5y 8
3x + 4y 4
x + 2y 2
A:
B:
C:
D:

Systems of Linear Equations / Inequalities
Objective:
Students should be able to solve
systems of linear equations and
inequalities
LinearSystemswithManyorNoSolutions
Solvethelinearsystem
x2y+3
x2y3
2x4y7
Solvethefirstequationforx.
Substitutetheexpression

Exercises
Solve the following linear programming problems by graphing.
(a) Find the maximum value of p = 2x + 3y subject to
2x + y 15
x + 3y 20
x 0, y 0
(b) Find the minimum value of c = 4x + 5y subject to
x + 2y 10
2x + 3y 18
x 0, y 0
(c) Find the maximu

Linear Programming
Objective:
Students should be able to solve
linear programming problems
graphically
Linear Programming
Maximize p = ax + by
p = ax + by
Subject to:
some constraints
(i.e., region defined by linear
inequalities)
The solution:
If the so

CHAPTER
3
Linear Programming: Geometric Approach
OUTLINE
3.1 Systems of Linear
Inequalities
3.2 A Geometric Approach
to Linear Programming
Problems
3.3 Applications
Chapter Review
Chapter Project
Mathematical Questions
I
ts the weekend after midterms,