3.4 – Linear Programming

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y

3.4 – Linear ProgrammingEx. 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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y (x, y) x – y f(x,y)

3.4 – Linear ProgrammingEx. 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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y (x, y) x – y f(x,y)

(0.-4)

(3,5)

(3,-4)

3.4 – Linear ProgrammingEx. 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 > -4

x < 3

y < 3x – 4

f(x,y) = x – y (x, y) x – y f(x,y)

(0.-4) 0 – (-4) 4

(3,5)

(3,-4)

3.4 – Linear ProgrammingEx. 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 > -4

x < 3

y < 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 – Linear ProgrammingEx. 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 > -4

x < 3

y < 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

3.4 – Linear ProgrammingEx. 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 > -4

x < 3

y < 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

3.4 – Linear ProgrammingEx. 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 > -4

x < 3

y < 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 @ (3,-4)

3.4 – Linear ProgrammingEx. 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 > -4

x < 3

y < 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 @ (3,-4)

3.4 – Linear ProgrammingEx. 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 > -4

x < 3

y < 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 @ (3,-4)Min of -2 @ (3,5)