linear programming 1.3 m3. -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 warm-up graph the system
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Linear Linear
Programming
Programming1.3 M31.3 M3
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-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Warm-UpGraph the system.
x 0
y 0
y 3x 2
y x 4
![Page 3: Linear Programming 1.3 M3. -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 Warm-Up Graph the system](https://reader036.vdocuments.us/reader036/viewer/2022082818/56649ec55503460f94bcfcf1/html5/thumbnails/3.jpg)
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Graph the system.
x 0
y 0
y 3x 2
y x 4
![Page 4: Linear Programming 1.3 M3. -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 Warm-Up Graph the system](https://reader036.vdocuments.us/reader036/viewer/2022082818/56649ec55503460f94bcfcf1/html5/thumbnails/4.jpg)
What
is
What
is
Linear
Linear
Progra
mm
ing
Progra
mm
ing ??
1.1.Way to maximize or
Way to maximize or minimize a linear
minimize a linear objective function
objective function2.2.Has constraint
Has constraint inequalitiesinequalities3.3.Solutions (intersections)
Solutions (intersections)
of the constraints are
of the constraints are
possible solutions to the
possible solutions to the
objective function
objective function (equation)(equation)
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Genera
l Exa
mple
Genera
l Exa
mple
Concession Stand that Sells
Concession Stand that Sells
Hot Dogs & Hamburgers
Hot Dogs & Hamburgers
You have a certain amount
You have a certain amount
of money to buy them.
of money to buy them.
Only so many hot dogs will
Only so many hot dogs will
fit on the grill. (same
fit on the grill. (same
with hamburgers)
with hamburgers)You want to know how
You want to know how much of each to buy to
much of each to buy to
give you the
give you the Maximum
Maximum
Profit.Profit.
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You H
ave
3
You H
ave
3
Unkn
ow
ns
Unkn
ow
ns
Hot Dogs (x)
Hot Dogs (x)Hamburgers (y)
Hamburgers (y)Maximum Profit (z)
Maximum Profit (z)2 unknowns are graphed
2 unknowns are graphed
on a coordinate plane.
on a coordinate plane.
3 unknowns will create a
3 unknowns will create a
3 dimensional graph.
3 dimensional graph. (x, y, z)(x, y, z)
x
z
y
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To S
olv
eTo
Solv
e
1.1.Graph the Inequalities
Graph the Inequalities
2.2.Identify the solutions
Identify the solutions
(intersections)
(intersections)3.3.Substitute the solutions
Substitute the solutions
into the objective
into the objective function (equation)
function (equation)4.4.Look for the answer to
Look for the answer to
the problem.
the problem. (maximum or minimum
(maximum or minimum
value)value)
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003 15
4 16
xyx yx y
Find the minimum value and the maximum value of
the objective function C = 3x + 2y subject to the following constraints.
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Unders
tandin
g
Unders
tandin
g
wit
h P
lay-
doh
wit
h P
lay-
doh
1.1.Place you play-doh on top
Place you play-doh on top
of your graph.
of your graph.2.2.Trim the edges of your play-
Trim the edges of your play-
doh to be constraint
doh to be constraint
equations.equations.3.3.The linear programming
The linear programming
concept builds a 3D model
concept builds a 3D model
that has its top base sliced
that has its top base sliced
at an angle. The
at an angle. The highest highest
vertexvertex is at the
is at the maximum
maximum
value value and the lowest
and the lowest
vertex is at the minimum
vertex is at the minimum
value. value. 4.4.Identify the maximum
Identify the maximum
vertex and slice the top
vertex and slice the top
base at an angle towards
base at an angle towards
your minimum vertex.
your minimum vertex.