3.4

1
3.4 Linear Programming

2
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

3
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

4
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

5
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

6
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

7
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

8
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

9
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

10
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

11
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

12
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

13
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)



14
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)
(0.-4)
(3,5)
(3,-4)
15
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)
(0.-4) 0 (-4) 4
(3,5)
(3,-4)
16
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)
(0.-4) 0 (-4) 4
(3,5) 3 5 -2
(3,-4)
17
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)
(0.-4) 0 (-4) 4
(3,5) 3 5 -2
(3,-4) 3 (-4) 7
18
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)
(0.-4) 0 (-4) 4
(3,5) 3 5 -2
(3,-4) 3 (-4) 7
19
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)
(0.-4) 0 (-4) 4
(3,5) 3 5 -2
(3,-4) 3 (-4) 7
Max of 7 _at_ (3,-4)
20
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)
(0.-4) 0 (-4) 4
(3,5) 3 5 -2
(3,-4) 3 (-4) 7
Max of 7 _at_ (3,-4)
21
3.4 Linear Programming

• Ex. 1 Graph the system of inequalities. Name
  the coordinates of the vertices of the feasible
  region. Find the max min values of the given
  function for this region.
• y gt -4
• x lt 3
• y lt 3x 4
• f(x,y) x y

(x, y) x y f(x,y)
(0.-4) 0 (-4) 4
(3,5) 3 5 -2
(3,-4) 3 (-4) 7
Max of 7 _at_ (3,-4)
Min of -2 _at_ (3,5)