1) The document presents a mathematical optimization model to maximize the objective function of X + 4Y ≤ 60, X + Y ≤ 30, X ≥ 0, Y ≥ 0, where X and Y are integers. 2) By drawing the graphs of the equations and finding their intersection point, the optimal solution is determined to be X = 20, Y = 10. 3) Plugging the optimal values into the objective function Z = 1500X + 3000Y gives the maximum value of 60,000.

1. DUAARJUNA ALWI MUTIATUL ULA
TYAS FALATEHANDWI NUR
YOLANDA FRANCISKA

2. 3 . A ) T E N T U K A N N I L A I O P T I M U M DA R I
M O D E L M AT E M AT I K A
X + 4 Y ≤ 6 0
X + Y ≤ 3 0
X ≥ 0 , Y ≥ 0 ; X , Y € C
F U N G S I O B J E K T I F M E M A K S I M U M K A N

3. x + 4y = 60 x + y = 30
Menggambar Grafik
Pada persamaan x + 4y = 60 dan x + y = 30
x 0 60
y 15 0
( x , y ) ( 0 , 15 ) ( 60 , 0 )
x 0 30
y 30 0
( x , y ) ( 0 , 30 ) ( 30 , 0 )

4. Mencari titik potong kedua garis
x + 4y = 60
x + y = 30
3y = 30
y = 10
x + y = 30
x +10 = 30
x = 30 – 10
x = 20
Koordinat titik potong adalah ( 20 , 10 )

5. 5 10 15 20 25 30 35 40 45 50 55 60 65 70
5
10
15
25
20
10
30
40
35
45
5
0
5
5
60
y
x
0
( 20,10 )
( 60,0 )
(30,0)
(0,15)
(0,30)
Titik Pojok Z = f ( x , y ) = 1500x +
( 0 , 0 ) 0
( 30 , 0 ) 45.000
( 20 , 10 ) 60.000
( 0 , 15 ) 45.000
Jadi nilai
maksimum dari
model matematika
adalah 60.000

6. THANKS!