The problem is to determine the optimal production levels of shoes, bags and wallets to maximize profit given constraints on available labor hours (240) and raw materials (400kg). The summary provides the production details and pricing for each product. The full problem is written down separately to be solved at home using manual, Excel and QM methods through the first iteration of primal and dual solutions.

1. PRIMAL
MEJA KURSI
PEKERJAAN (X1) (X2) JAM KERJA
PAINTING 2 1 100
CARPENTRY 4 3 240
KEUNTUNGAN 7 5
FUNGSI TUJUAN Z = 7 X1 + 5 X2
KENDALA 2 X1 + X2 <= 100
4 X1 + 3X2 <= 240
X1 , X2 >= 0

2. FUNGSI TUJUAN Z -7 X1 - 5 X2 = 0
KENDALA 2 X1 + X2 + S1 + 0 S2 = 100
4 X1 + 3X2 + 0S1+ S2 = 240
X1 , X2 >= 0
BASIS X1 X2 S1 S2 SOLUSI
Z -7 -5 0 0 0
S1 2 1 1 0 100
S2 4 3 0 1 240

3. BASIS X1 X2 S1 S2 SOLUSI
Z -7 -5 0 0 0
S1 2 1 1 0 100
S2 4 3 0 1 240
Kolom kunci Angka kunci Baris kunci
BASIS X1 X2 S1 S2 SOLUSI
Z
X1 2/2= ½= ½= 0/2= 100/2=
1 1/2 1/2 0 50
S2

4. BASIS X1 X2 S1 S2 SOLUSI
Z -7-(-7X1)= -5-(7X1/2)= 0-(-7x1/2)= 0-(-7x0)= 0-(-7x50)=
0 -1 1/2 3 1/2 0 350
X1 2/2= ½= ½= 0/2= 100/2=
1 1/2 1/2 0 50
S2 4-(4x1)= 3-(4x1/2)= 1-(4x0)= 1-(4x1/2)= 240-(4x50)=
0 1 1 -1 40
Kolom kunci Angka kunci Baris kunci
BASIS X1 X2 S1 S2 SOLUSI
Z
X1
X2 0/1= 1/1= 1/1= -1/1= 40/1=
0 1 1 -1 40

5. BASIS X1 X2 S1 S2 SOLUSI
0-(-1 1/2x0)= -1 ½-(-1 1/2x1)= 3 ½-(-1 1/2x1)= 3 ½-(-1 1/2x-1)= 350-(-1 1/2x40)=
Z
0 0 5 1 1/2 410
1-(1/2x0)= ½-(1/2 x 1)= 0-(1/2x1)= ½-(1/2X-1)= 50-(1/2x40)=
X1
1 0 -1/2 1 30
0/1= 1/1= 1/1= -1/1= 40/1=
X2
0 1 1 -1 40
KESIMPULAN X1 = 30
X2 = 40
Z = 410

6. EXCELL
Target Cell (Max)
Cell Name Original Value Final Value
$B$4 OBJ X1 0 410
Adjustable Cells
Cell Name Original Value Final Value
$B$2 X1 0 30
$C$2 X2 0 40
Constraints
Cell Name Cell Value Formula Status Slack
$B$5 P X1 100$B$5<=$C$5 Binding 0
$B$6 C X1 240$B$6<=$C$6 Binding 0
$B$2 X1 30$B$2>=0 Not Binding 30
$C$2 X2 40$C$2>=0 Not Binding 40

7. DUAL
MEJA KURSI
PEKERJAAN JAM KERJA
PAINTING (Y2) 2 1 100
CARPENTRY (Y1) 4 3 240
KEUNTUNGAN 7 5
TUJUAN W = 240Y1 + 100 Y2
KENDALA 4 Y1 + 2 Y2 <= 7
3 Y1 + Y2<= 5
Y1,Y2 >=0

8. TUJUAN W - 240Y1 -100 Y2 = 0
KENDALA 4 Y1 + 2 Y2 + S1 + 0 S2 = 7
3 Y1 + Y2 + 0S1 + S2 = 5
Y1,Y2 >=0
BASIS Y1 Y2 S1 S2 SOLUSI
W -240 -100 0 0 0
S1 4 2 1 0 7
S2 3 1 0 1 5

9. BASIS Y1 Y2 S1 S2 SOLUSI
W -240 -100 0 0 0
S1 4 2 1 0 7
S2 3 1 0 1 5
Kolom kunci Angka kunci Baris kunci
BASIS Y1 Y2 S1 S2 SOLUSI
W
S1
3/3= 1/3= 0/3= 1/3= 5/3=
Y1 1 1/3 0 1/3 1 2/3

10. BASIS Y1 Y2 S1 S2 SOLUSI
W -240-(-240x1)= -100-(-240x1/3)= 0-(-240x0)= 0-(-240x1/3)= 0-(-240x1 2/3)=
0 -20 0 80 400
S1 4-(4x1)= 2-(4x1/3)= 1-(4x0)= 0-(4x1 2/3)= 7- (4x 1 2/3)=
0 2/3 1 - 1 1/3 1/3
3/3= 1/3= 0/3= 1/3= 5/3=
Y1 1 1/3 0 1/3 1 2/3
Kolom kunci Angka kunci Baris kunci
BASIS Y1 Y2 S1 S2 SOLUSI
W
Y2 0 : 2/3= 2/3 : 2/3 = 1 : 2/3 = -1 1/3 : 2/3 = 1/3 : 2/3 =
0 1 1½ -2 1/2 1/2
Y1

11. BASIS Y1 Y2 S1 S2 SOLUSI
W 0-(-20x0)= -20-(-20x1 ½)= 0(-20x1 ½)= 80-(-20x-2 ½)= 400-(-20x1/2)=
0 0 5 1 1/2 410
Y2 0 : 2/3= 2/3 : 2/3 = 1 : 2/3 = -1 1/3 : 2/3 = 1/3 : 2/3 =
0 1 1½ -2 1/2 1/2
1-(1/3x0)= 1/3-(1/3x1)= 0-(1/3x1 1/3-(1/3x-2 ½)= 1 2/3-(1/3x1/2)=
Y1 1 0 ½)= 1 1 1/2
- 1/2
HASIL W = 410
Y2 = ½
Y1 = 1 1/2

12. Target Cell (Max)
Cell Name Original Value Final Value
$B$4 TUJUAN Y1 0 410
Adjustable Cells
Cell Name Original Value Final Value
$B$2 Y1 0 1.5
$C$2 Y2 0 0.5
Constraints
Cell Name Cell Value Formula Status Slack
$B$5 X1 Y1 7$B$5<=$C$5 Binding 0
$B$6 X2 Y1 5$B$6<=$C$6 Binding 0
$C$2 Y2 0.5$C$2>=0 Not Binding 0.5
$B$2 Y1 1.5$B$2>=0 Not Binding 1.5

14. LATIHAN LINIER PROGRAMING
SEBUAH PERUSAHAAN MENGHASILKAN TIGA JENIS PRODUK YAITU SEPATU, TAS DAN DOMPET
JUMLAH WAKTU KERJA BURUH YANG TERSEDIA ADALAH 240 JAM KERJA DAN BAHAN MENTAH
400 KG DAN HARGA MASING-MASING PRODUK ADALAH SEPERTI TERSAJI PADA TABEL BERIKUT:
PRODUKSI A HARGA
BURUH (JAM) BAHAN (KG/UNIT) PER UNIT
SEPATU 5 4 3
TAS 2 6 5
DOMPET 4 3 2
BERAPAKAH JUMLAH MASING-MASING PRODUK YANG HARUS DIHASILKAN AGAR
KEUNTUNGAN MAKSIMUM DAN BIAYA MINIMUM?
BUAT SAMPAI ITERASI PERTAMA PRIMAL DAN DUAL
CATAT SOALNYA PAKAI KERTAS LAIN KEMUDIAN SELESAIKAN DIRUMAH
(MANUAL, EXCELL DAN QM)