Linear Program
Solving problem of linear program
Graph of solution set in Linear unequation system
Graph of solution set in linear unequation system
Graph of linear unequation in one variable
Example :
Determine the solution area of unequation
x 1
y
Answer:
3
2
DP
1
-3 -2 -1
x
0
1
2
3
-2
Hal.: 2
Program linear
Adaptif
Graph of solution set in Linear unequation system
2. Determine the solution area of unequation
1  y  2
y
3
2
1
-3 -2 -1
DP
0
1
2
x
3
-2
Hal.: 3
Program linear
Adaptif
Graph of solution set in Linear unequation system
2. Graph of linear unequation in two variables
Example 1 :
Find the solution area of unequation 2x + 3y < 6
y
1. Picture 2x + 3y = 6
2
2. Examining the point
DP
1
x
1
Hal.: 4
2
3
Program linear
Adaptif
Graph of solution set in Linear unequation system
Example 2 :
Find the solution area of unequation
x + y > 7
y
1. Picture x + y = 7
2. Examining the point
DP
x
1 2 3 4 5 6 7
Hal.: 5
Program linear
Adaptif
Graph of solution set in Linear unequation system
Example 3 :
Find the solution area of
unequation x + y > 7 and x +
2y < 10
y
7
1. Picture x + y = 7
6
5
2. Picture x + 2y = 10
4
3. Examining the point
DP
3
2
1
x
1
Hal.: 6
2
3
4
5
6
7
8 9 10
Program linear
Adaptif
MATH MODEL
Base Competence :
Determining the math model from story test
Indicators
:
1. Story test (verbal sentence) is translated into math
sentence
2. Determining a solution area of math sentence
Hal.: 7
Program linear
Adaptif
MATH MODEL
MAKING MATH MODEL
• See the exercise below :
• A plane has not more than 300 seats, consist of economic
and VIP class.
The passengers of economic class may bring about 3kg
luggage and VIP class about 5kg luggage. While the plane is
able to bring only 1200,
Ticket of economic class gives benefit Rp 100.000.00 and
VIP class about Rp 200.000,00
So how much is the maximum benefit of plane ticketing?
Hal.: 8
Program linear
Adaptif
MATH MODEL
The statement above can be made two tables as follow:
Economic
class size (x)
Seats
Baggage
Hal.: 9
VIP class size
(y)
maximum
x
y
300
3x
5y
1200
Program linear
Adaptif
MODEL MATEMATIKA
SISTEM PERTIDAKSAMAAN LINEAR
PERMASALAHAN TERSEBUT ADALAH
Hal.: 10
x  y  300
Pertidaksamaan (1)
3 x  5 y  1200
Pertidaksamaan (2)
x 0
Pertidaksamaan (3)
y0
Pertidaksamaan (4)
Program linear
Adaptif
MATH MODEL
LINEAR UNEQUATION SYSTEM
THE PROBLEMS ARE
Hal.: 11
x  y  300
Unequation (1)
3 x  5 y  1200
Unequation (2)
x 0
Unequation (3)
y0
Unequation (4)
Program linear
Adaptif
OPTIMUM VALUE
Hal.: 12
Program linear
Adaptif
OPTIMUM VALUE
• x + y 300
y
300
DP
x
0
Hal.: 13
300
Program linear
Adaptif
OPTIMUM VALUE
y
3x + 5y  1200
240
DP
x
0
Hal.: 14
400
Program linear
Adaptif
OPTIMUM VALUE
y
x + y  300
3x + 5y  1200
300
240
(150, 150)
DP
x
0
Hal.: 15
300
400
Program linear
Adaptif
OPTIMUM VALUE
• x + y  300
y
• 3x + 5y
 1200
0
• y 0
•x
300
240
(150,150)
DP
X
0
Hal.: 16
300
400
Program linear
Adaptif
OPTIMUM VALUE
FINDING THE OPTIMUM VALUE BY CORNER POINT
EXAMINATION
•x+y
300
• 3x + 5y
y
 1200
0
• y 0
•x
A(0,240)
E(150,150)
POINT
Titik
ff :: xx +
+ 2y
2y
A(0,240)
0+2.240=480
D(300,0)
300+2.0=300
E(150,150)
150+2.150=450
max
DP
X
0
Hal.: 17
D(300,0)
Program linear
Adaptif
INVESTIGATED LINE
FINDIN THE OPTIMUM VALUE BY INVESTIGATED LINE
y
C(0,300)
f : x + 2y
A(0,240)
A(0,240)
E(150,150)
DP
x
D(300,0) B(400,0)
0
f : x + 2y
Hal.: 18
Program linear
Adaptif
OPTIMUM VALUE
A
B
C
D
Rp 30.000.000,00
SORRY YOU
ARE FALSE
SORRY,
YOU’RE STILL
FALSE
Rp 35.000.000,00
STILL FALSE
Rp 45.000.000,00
Rp48.000.000,00
GREAT! YOU’RE RIGHT
Hal.: 19
Program linear
Adaptif
Exercise of Linear program:
Width of parking area is 360 meter square.
The average width of a car is 6 meter
square, and for the bus is about 24 meter
square. The parking area cannot take more
than 30 vehicles.
If the car quantity is x and the number of
bus is y. then determine the unequation
system
Hal.: 20
Program linear
Adaptif
GOOD LUCK!
THANKS FOR THE
ATTENTION
Hal.: 21
Program linear
Adaptif