Tugas 2 Analisis Kebutuhan Pergerakan

(1)

SI-4141 ANALISIS KEBUTUHAN PERGERAKAN SI-4141 ANALISIS KEBUTUHAN PERGERAKAN

TUGAS 2

Dosen :

Prof. Ir. Ofyar Z. Tamin, M.Sc., Ph.D.

Disusun oleh :

Feri Triana !ar"ami Sia#ian

$%&$2&$'

PROGRAM STUDI TEKNIK SIPIL PROGRAM STUDI TEKNIK SIPIL FA

FAKULTKULTAS TEKNIK AS TEKNIK SIPIL DAN SIPIL DAN LINGKUNGANLINGKUNGAN INSTITUT TEKNOLOGI BANDUNG

INSTITUT TEKNOLOGI BANDUNG

2015

(2)

(3)

Metode Ana!t!" Metode Ana!t!"

$.

$. a. (i)a hanya. (i)a hanya ruas $ yan# ea ruas $ yan# ero*ero*erasi, erasi, era*a arura*a arus yan# "ers yan# "er+ai an+ai an"ara A "ara A an - an eran - an era*a a)a*a a)"u"u "em*uhnya/

"em*uhnya/

. (i)a hanya ruas 2 yan# ero

. (i)a hanya ruas 2 yan# ero*erasi, era*a arus yan# "er*erasi, era*a arus yan# "er+ai an"ara A +ai an"ara A an - an era*a a)"uan - an era*a a)"u "em*uhnya/

"em*uhnya/

c. (i)a hanya ruas $

c. (i)a hanya ruas $ an ruas 2 ero*erasi ersama0sama, era*a arus an ruas 2 ero*erasi ersama0sama, era*a arus yan# "er+ai an"ara A yan# "er+ai an"ara A an -,an -, an era*a a)"u

an era*a a)"u "em*uhnya/"em*uhnya/ . To

. Tolon# ie1aluasi mana yan# ana *ilih $, 2, lon# ie1aluasi mana yan# ana *ilih $, 2, a"au $ an 2a"au $ an 2 2.

2. AsumAsumsi)an si)an "er+"er+ai ai *eni*enin#)an#)a"an. "an. !i"u!i"un# n# *oin *oin a0f a0f a.

a. UsiUsia )era )er+a a+a an se)n se)olaolah arh ari '&3 mi '&3 men+en+ai $ai $&&&&33 .

. 4a*an#an )er+a ari 2%.&&& m4a*an#an )er+a ari 2%.&&& men+ai 5&.&&&en+ai 5&.&&& 5.

5. Den#Den#an )onan )onisi siisi sis"em )es"em )e#ia"#ia"an se*ean se*er"i no. $r"i no. $. !i"u. !i"un# An# A0F +i)a0F +i)a a.

a. $ o$ o1er1erlay lay sehsehin#in##a I#a ITP TP menmen+a+ai &.i &.$$ .

. $ ilear)an sehin##$ ilear)an sehin##a )a*asi"as men+ai 6&a )a*asi"as men+ai 6&&& )en7+am&& )en7+am 8.

8. DeDen#n#an an *e*eruruaahahann demand demand an an supply supply a.

a. UsiUsia )era )er+a a+a an se)n se)olaolah arh ari '&3 mi '&3 men+en+ai $ai $&&&&33 .

. 4a*an#an )er+a ari 2%.&&& m4a*an#an )er+a ari 2%.&&& men+ai 5&.&&&en+ai 5&.&&& c.

c. $ o$ o1er1erlay lay sehsehin#in##a I#a ITP TP menmen+a+ai &.i &.$$ .

. $ i$ ilearlear)an s)an sehinehin##a )##a )a*asia*asi"as m"as men+ai en+ai 6&&& 6&&& )en)en7+am7+am

(aa: (aa:

$. Den#an memasu))an a"a *o*ulasi, *ersen"ase usia )er+a, la*an#an )er+a, an asumsi o)u*ansi *er $. Den#an memasu))an a"a *o*ulasi, *ersen"ase usia )er+a, la*an#an )er+a, an asumsi o)u*ansi *er )enaraan 9 $ )enaraan  2

)enaraan 9 $ )enaraan  2 oran#;, ia*a" hal eri)u" inioran#;, ia*a" hal eri)u" ini

P

PA

A

=

9090

100

x

6000060000

=

5400054000

orang

=

2700027000

kendaraan

AB

=

2500025000

_orang

=

1250012500

_kendaraan

Searan *er#era)an ian##a* men#i)u"i hu)um

Searan *er#era)an ian##a* men#i)u"i hu)um gravity gravity sea#ai eri)u". sea#ai eri)u".

Q Q_AB_AB== P P_A_A x x AA_B_B T T _Q_Q AB AB xx k k

(4)

Q Q_AB_AB==2700027000 x x1250012500 T T _Q_Q AB AB x x0.00250.0025

Q

_AB_AB

=

843750843750

T

QQ AB AB

!uun#an an"ara a)"u "em*uh en#an 1olume

!uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) arus lalu lin"as un"u) se"ia* ru"enya iasumsi)anse"ia* ru"enya iasumsi)an men#i)u"i rumus

men#i)u"i rumus Davidson Davidson sea#ai eri)u". sea#ai eri)u".

T

_Q_Q AB AB

=

T

_o_o

[[

1 1

−(

11

−

_a

))

Q

C

1 1

−

Q

C

]]

!uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) ru"e $ ia*a" se*er"i eri)u". !uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) ru"e $ ia*a" se*er"i eri)u".

T

_Q_Q 1 1

=

25 25

[[

1 1

−

−((

11

−

0.40.4

))

Q

5000 5000 1 1

−

Q

5000 5000

]]

T

_Q_Q₁₁

=

2525

[[

5000 5000

−(

0.60.6

))

Q

5000 5000

−

_Q

]]

!uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) ru"e 2 ia*a" se*er"i eri)u" !uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) ru"e 2 ia*a" se*er"i eri)u"

T

_Q_Q₂₂

=

4040

[[

1 1

−(

11

−

0.90.9

))

Q

3000 3000 1 1

−

Q

3000 3000

]]

T

_Q_Q 2 2

=

40 40

[[

30003000

−(

0.10.1

))

Q

3000 3000

−

_Q

]]

(5)

<emuian ila)u)an susi"usi an"ara *ersamaan searan *er#era)an en#an huun#an an"ara

<emuian ila)u)an susi"usi an"ara *ersamaan searan *er#era)an en#an huun#an an"ara a)"ua)"u "em*uh en#an 1olume arus lalu

"em*uh en#an 1olume arus lalu lin"as un"u) se"ia* ru"enyalin"as un"u) se"ia* ru"enya

• • u"e $u"e $ 843750 843750

Q

11

=

2525 50005000

−(

0.60.6

))

Q

11 5000 5000

−

_Q

₁₁ 843750 843750

Q

11

=

[[

125000125000

−

1515

Q

11 5000 5000

−

_Q

₁₁

]]

421875 421875

_x

101044

−

843750843750

_Q

₁₁

=

125000125000

_Q

₁₁

−

1515

_Q

₁₁22 15 15

_Q

₁₁22

−

968750968750

_Q

₁₁

+

421875421875

_x

101044

=

00

Q

11 1 1

=

59886.98759886.987

kendaraan

jam

… … … …

((

tidak

tidak memenu

memenuhi

hi

))

Q

11 2 2

=

4696.3454696.345

kendaraan

jam

… … … …

((

memenuhi

))

Sehin##a ia*a")an a)"u "em*uh un"u) ru"e

Sehin##a ia*a")an a)"u "em*uh un"u) ru"e $ en#an sea#ai eri)u".$ en#an sea#ai eri)u".

T

_Q_Q AB AB

=

843750843750

Q

_AB_AB

T

_Q_Q AB AB

=

843750 843750 4696.345 4696.345

=

179.66179.66

menit

• • u"e 2u"e 2

(6)

843750

Q

2

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

843750

Q

2

=

[

120000

−

4

Q

2 3000

−

_Q

₂

]

253125

_x

104

−

843750

_Q

₁

=

120000

_Q

₂

−

4

_Q

₂2 4

_Q

₂2

−

963750

_Q

₂

+

253125

_x

104

=

0

Q

2 1

=

238281.768

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

2 2

=

2655.731

kendaraan

jam

… … … …

(

memenuhi

)

Sehin##a ia*a")an a)"u "em*uh un"u) ru"e 2 en#an sea#ai eri)u".

T

_Q AB

=

843750

Q

_AB

T

_Q AB

=

843750

2655.731

=

317.7091

menit

• u"e $ an ru"e 2 sama0sama ero*erasi

Syarat batas

(

1

)

:

_Q

AB

=

Q

1

+

Q

2

Syarat batas

(

2

)

:

_T

Q1

=

T

Q2

(

kondisi keseimbangan Wardrop

)

[

125000

−

15

_Q

₁ 5000

−

_Q

₁

]

=

[

120000

−

4

_Q

₂ 3000

−

_Q

₂

]

(7)

75000

_Q

₁

+

11

_Q

₁

_Q

₂

=

22500

_x

104

+

105000

_Q

₂

Q

1

(

75000

+

11

Q

2

)=

22500

x

10 4

+

105000

_Q

₂ Q1= 22500 x104₊105000Q2 75000₊11Q₂

<emuian *ersamaan =$ isusi"usi)an "erhaa* *ersamaan T=

T

_Q AB

=

843750

Q

1

+

Q

2 843750

Q

1

+

Q

2

=

120000

−

4

Q

2 3000

−

_Q

₂ 843750 22500

_x

104

+

105000

_Q

₂ 75000

+

11

_Q

₂

+

Q

2

=

120000

−

4

Q

2 3000

−

_Q

₂ 843750 22500

_x

104

+

105000

_Q

₂

+

_Q

₂

(

75000

+

11

_Q

₂

)

75000

+

11

_Q

₂

=

120000

−

4

Q

2 3000

−

_Q

₂ 843750 22500

_x

104

+

105000

_Q

₂

+

75000

_Q

₂

+

11

_Q

₂2 75000

+

11

_Q

₂

=

120000

−

4

Q

2 3000

−

_Q

₂ 843750

(

75000

+

11

_Q

₂

)

22500

_x

104

+

105000

_Q

₂

+

75000

_Q

₂

+

11

_Q

₂2

=

120000

−

4

_Q

₂ 3000

−

_Q

₂ 6.328

_x

1010

+

9281250

_Q

₂ 22500

_x

104

+

180000

_Q

₂

+

11

_Q

₂2

=

120000

−

4

_Q

₂ 3000

−

_Q

₂

(8)

Q

2 1

=

262115.0143

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

2 2

=

2055.433

kendaraan

jam

… … … …

(

memenuhi

)

Q

2 3

=−

6869.310

kendar aan

jam

… … … …

(

tidak memenuhi

)

Se"elah men#e"ahui nilai =2 ma)a icari nilai =$

Q

1

=

22500

_x

104

+

105000

_Q

₂ 75000

+

11

_Q

₂

Q

1

=

22500

_x

104

+

105000

(

2055.433

)

75000

+

11

(

2055.433

)

Q

1

=

22500

_x

104

+

215820465 75000

+

22609.763

Q

1

=

440820465 97609.763

=

4516.151

kendaraan

jam

Den#an mena*a")an nilai =$ an =2 ma)a a*a" ihi"un# nilai T=

T

_Q AB

=

843750

Q

1

+

Q

2

T

_Q AB

=

843750

4516.151

+

2055.433

=

128.393

menit

Pen#er+aan yan# ia"as a*a" isim*ul)an se*er"i eri)u".

u"e =$9)enaraan7+am; =29)enaraan7+am; T=9meni";

$ 4696.345 ₀ 179.66

2 0 2655.731 317.7091

(9)

-erasar)an hasil yan# ia"as ia*a")an aha ru"e yan# i*ilih aalah ru"e $> ru"e 2. !al ini i)arena)an a)"u "em*uh yan# ia*a")an leih )ecil ianin#)an en#an yan# lain an memili)i arus lalu lin"as yan# leih )ecil *ula.

2. Asumsi "er+ai *enin#)a"an

a. Usia )er+a an se)olah ari '&3 men+ai $&&3 . 4a*an#an )er+a ari 2%.&&& men+ai 5&.&&&

Den#an memasu))an a"a *o*ulasi, *ersen"ase usia )er+a, la*an#an )er+a, an asumsi o)u*ansi *er )enaraan 9 $ )enaraan  2 oran#;, ia*a" hal eri)u" ini

PA

=

100

x

60000

=

60000

orang

=

30000

kendaraan

AB

=

30000

_orang

=

15000

_kendaraan

Searan *er#era)an ian##a* men#i)u"i hu)um gravity sea#ai eri)u".

Q_AB= P_A x A_B T _Q AB x k

Q

_AB

=

30000

x

15000

T

_Q AB

x

0.0025 Q_AB= 1125000 T _Q AB

!uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) se"ia* ru"enya iasumsi)an men#i)u"i rumus Davidson sea#ai eri)u".

T

_Q AB

=

T

_o

[

1

−(

1

−

_a

)

Q

C

1

−

Q

(10)

!uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) ru"e $ ia*a" se*er"i eri)u".

T

_Q₁

=

25

[

1

−(

1

−

0.4

)

Q

5000 1

−

Q

5000

]

T

_Q₁

=

25

[

5000

−(

0.6

)

Q

5000

−

_Q

]

!uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) ru"e 2 ia*a" se*er"i eri)u"

T

_Q 2

=

40

[

1

−(

1

−

0.9

)

Q

3000 1

−

Q

3000

]

T

_Q 2

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

<emuian ila)u)an susi"usi an"ara *ersamaan searan *er#era)an en#an huun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) se"ia* ru"enya

• u"e $ 1125000

Q

1

=

25

[

5000

−(

0.6

)

Q

1 5000

−

_Q

₁

]

1125000

Q

1

=

[

125000

−

15

Q

1 5000

−

_Q

₁

]

5625

_x

106

−

1125000

_Q

₁

=

125000

_Q

₁

−

15

_Q

₁2

(11)

15

_Q

₁2

−

1250000

_Q

₁

+

5625

_x

106

=

0

Q

1 1

=

78559.906

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

1 2

=

4773.427

kendaraan

jam

… … … …

(

memenuhi

)

Sehin##a ia*a")an a)"u "em*uh un"u) ru"e $ en#an sea#ai eri)u".

T

_Q AB

=

1125000

Q

_AB

T

_Q AB

=

1125000 4773.427

=

235.679

menit

• u"e 2 1125000

Q

2

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

1125000

Q

2

=

[

120000

−

4

Q

2 3000

−

_Q

₂

]

3375

_x

106

−

1125000

_Q

₁

=

120000

_Q

₂

−

4

_Q

₂2 4

_Q

₂2

−

1245000

_Q

₂

+

3375

_x

106

=

0

Q

2 1

=

308515.126

kendaraan

(12)

Q

2 2

=

2734.874

kendaraan

jam

… … … …

(

memenuhi

)

T

_Q AB

=

1125000

Q

_AB

T

_Q AB

=

1125000

2734.874

=

411.353

menit

Syarat batas

(

1

)

:

_Q

AB

=

Q

1

+

Q

2

Syarat batas

(

2

)

:

_T

Q1

=

T

Q2

(

kondisi keseimbangan Wardrop

)

[

125000

−

15

_Q

₁ 5000

−

_Q

₁

]

=

[

120000

−

4

_Q

₂ 3000

−

_Q

₂

]

37500

_x

104

−

45000

_Q

₁

−

125000

_Q

₂

+

15

_Q

₁

_Q

₂

=

60000

_x

104

−

20000

_Q

₂

−

120000

_Q

₁

+

4

_Q

₁

_Q

₂ 75000

_Q

₁

+

11

_Q

₁

_Q

₂

=

22500

_x

104

+

105000

_Q

₂

Q

1

(

75000

+

11

Q

2

)=

22500

x

10 4

+

105000

_Q

₂

Q

1

=

22500

_x

104

+

105000

_Q

₂ 75000

+

11

_Q

₂

T

_Q AB

=

1125000

Q

1

+

Q

2

(13)

1125000

Q

1

+

Q

2

=

120000

−

4

Q

2 3000

−

_Q

₂ 1125000 22500

_x

104

+

105000

_Q

₂ 75000

+

11

_Q

₂

+

Q

2

=

120000

−

4

Q

2 3000

−

_Q

₂ 1125000 22500

_x

104

+

105000

_Q

₂

+

_Q

₂

(

75000

+

11

_Q

₂

)

75000

+

11

_Q

₂

=

120000

−

4

Q

2 3000

−

_Q

₂ 1125000 22500

_x

104

+

105000

_Q

₂

+

75000

_Q

₂

+

11

_Q

₂2 75000

+

11

_Q

₂

=

120000

−

4

Q

2 3000

−

_Q

₂ 1125000

(

75000

+

11

_Q

₂

)

22500

_x

104

+

105000

_Q

₂

+

75000

_Q

₂

+

11

_Q

₂2

=

120000

−

4

_Q

₂ 3000

−

_Q

₂ 8.4375

_x

1010

+

12375000

_Q

₂ 22500

_x

104

+

180000

_Q

₂

+

11

_Q

₂2

=

120000

−

4

_Q

₂ 3000

−

_Q

₂

Q

2 1

=−

273332.3812

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

2 2

=

2859.372

kendaraan

jam

… … … …

(

memenuhi

)

Q

2 3

=

2859.372

−

3259.438

kendaraan

jam

… … … …

(

tidak memenuhi

)

(14)

Q

1

=

22500

_x

104

+

105000

_Q

₂ 75000

+

11

_Q

₂

Q

1

=

22500

_x

104

+

105000

(

2859.372

)

75000

+

11

(

2859.372

)

Q

1

=

22500

_x

104

+

300234060 75000

+

31453.092

Q

1

=

525234060 106453.092

=

4933.9483

kendaraan

jam

T

_Q AB

=

843750

Q

1

+

Q

2

T

_Q AB

=

1125000

4933.9483

+

2859.372

=

144

.

354

menit

$ 4773.427 ₀ 235.679

2 0 2734.874 411.353

$>2 4933.9483 2859.372 144.354

-erasar)an hasil yan# ia"as ia*a")an aha ru"e yan# i*ilih aalah ru"e $> ru"e 2. !al ini i)arena)an a)"u "em*uh yan# ia*a")an leih )ecil ianin#)an en#an yan# lain. ?amun en#an

(15)

*en#o*erasian ru"e $ > ru"e 2 secara ersamaan, arus lalu lin"as yan# ia*a")an leih esar ianin#)an ru"e yan# lain. !al ini i)arena)an er"amahnya demand a)an )a*asi"as +alan yan# aa.

5. Den#an )onisi sis"em )e#ia"an se*er"i no. $. !i"un# A0F +i)a a. $ o1erlay sehin##a ITP men+ai &.$

. $ ilear)an sehin##a )a*asi"as men+ai 6&&& )en7+am

PA

=

90

100

x

60000

=

54000

orang

=

27000

kendaraan

AB

=

25000

_orang

=

12500

_kendaraan

Searan *er#era)an ian##a* men#i)u"i hu)um gravity sea#ai eri)u".

Q

_AB

=

27000

x

12500

T

Q AB

x

0.0025 Q_AB=843750 T _Q AB

T

_Q AB

=

T

_o

[

1

−(

1

−

_a

)

Q

C

1

−

Q

C

]

(16)

T

_Q 1

=

25

[

1

−(

1

−

0.1

)

Q

7000 1

−

Q

7000

]

T

_Q 1

=

25

[

7000

−(

0.9

)

Q

7000

−

_Q

]

!uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) ru"e 2 ia*a" se*er"i eri)u"

T

_Q 2

=

40

[

1

−(

1

−

0.9

)

Q

3000 1

−

Q

3000

]

T

_Q₂

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

• u"e $ 843750

Q

1

=

25

[

7000

−(

0.9

)

Q

7000

−

_Q

]

843750

Q

1

=

[

175000

−

22.5

Q

1 7000

−

_Q

₁

]

590625

_x

104

−

843750

_Q

₁

=

175000

_Q

₁

−

22.5

_Q

₁2 22.5

_Q

₁2

−

1018750

_Q

₁

+

590625

_x

104

=

0

(17)

Q

1 1

=

38450.887

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

1 2

=

6826.890

kendaraan

jam

… … … …

(

memenuhi

)

Sehin##a ia*a")an a)"u "em*uh un"u) ru"e $ en#an sea#ai eri)u".

T

_Q AB

=

843750

Q

_AB

T

_Q AB

=

843750 6826.890

=

123.592

menit

• u"e 2 843750

Q

2

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

843750

Q

2

=

[

120000

−

4

Q

2 3000

−

_Q

₂

]

253125

_x

104

−

843750

_Q

₁

=

120000

_Q

₂

−

4

_Q

₂2 4

_Q

₂2

−

963750

_Q

₂

+

253125

_x

104

=

0

Q

2 1

=

238281.768

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

2 2

=

2655.731

kendaraan

jam

… … … …

(

memenuhi

)

(18)

T

_Q AB

=

843750

Q

_AB

T

_Q AB

=

843750

2655.731

=

317.7091

menit

Syarat batas

(

1

)

:

_Q

AB

=

Q

1

+

Q

2

Syarat batas

(

2

)

:

_T

Q1

=

T

Q2

(

kondisi keseimbangan Wardrop

)

[

175000

−

22.5

_Q

₁ 7000

−

_Q

₁

]

=

[

120000

−

4

_Q

₂ 3000

−

_Q

₂

]

52500

_x

104

−

67500

_Q

₁

−

17 5000

_Q

₂

+

22.5

_Q

₁

_Q

₂

=

84 000

_x

104

−

14 000

_Q

₂

−

120000

_Q

₁

+

4

_Q

₁

_Q

₂ 52500

_Q

₁

+

18.5

_Q

₁

_Q

₂

=

31500

_x

104

+

161000

_Q

₂

Q

1

(

52500

+

18.5

Q

2

)=

31 500

x

10 4

+

161000

_Q

₂

Q

1

=

31500

_x

104

+

161000

_Q

₂ 52500

+

18.5

_Q

₂

T

_Q AB

=

843750

Q

1

+

Q

2 843750

Q

1

+

Q

2

=

120000

−

4

Q

2 3000

−

_Q

₂ 843750 31500

_x

104

+

161000

_Q

₂ 52500

+

18.5

_Q

₂

+

Q

2

=

120000

−

4

Q

2 3000

−

_Q

₂

(19)

843750 31500

_x

104

+

161000

_Q

₂

+

_Q

₂

(

52500

+

18.5

_Q

₂

)

52500

+

18.5

_Q

₂

=

120000

−

4

Q

2 3000

−

_Q

₂ 843750 31500

_x

104

+

161000

_Q

₂

+

52500

_Q

₂

+

18.5

_Q

₂2 52500

+

18.5

_Q

₂

=

120000

−

4

Q

2 3000

−

_Q

₂ 843750

(

52500

+

18.5

_Q

₂

)

31500

_x

104

+

161000

_Q

₂

+

52500

_Q

₂

+

18.5

_Q

₂2

=

120000

−

4

_Q

₂ 3000

−

_Q

₂ 4.429

_x

1010

+

15609375

_Q

₂ 31500

_x

104

+

213500

_Q

₂

+

18.5

_Q

₂2

=

120000

−

4

_Q

₂ 3000

−

_Q

₂

Q

2 1

=

230651.7947

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

2 2

=

1814.64084

kendaraan

jam

… … … …

(

memenuhi

)

Q

3 3

=−

3069.476

kendaraan

jam

… … … …

(

tidakmemenuhi

)

Q1= 31500_x104₊161000_Q₂ 52500₊18.5Q2 Q1

=

31500_x104

+

161000

(

1814.64084

)

52500

+

18.5

(

1814.64084

)

Q

1

=

31500

_x

104

+

292157040 52500

+

33570.84

(20)

Q

1

=

607157040

86070.84

=

7054.154

kendaraan

jam

T

_Q AB

=

843750

Q

1

+

Q

2

T

_Q AB

=

843750

7054.154

+

1814.64084

=

95.136

menit

$ 6826.890 ₀ 123.592

2 0 2655.731 411.353

$>2 7054.154 1814.64084 95.136

-erasar)an hasil yan# ia"as ia*a")an aha ru"e yan# i*ilih aalah ru"e $. Da*a" iliha" aha a)"u "em*uh ru"e $>2 leih ce*a" ianin#)an en#an ru"e $. ?amun, arus lalu lin"as un"u) ru"e $ un"u) *en#o*erasian )eua ru"e "elah meleihi )a*asi"asnya. !al "erseu" a*a" menyea)an )emace"an *aa ru"e $. Selain i"u, iaya yan# i)eluar)an un"u) meman#un ru"e $>2 a)an leih mahal

ianin#)an en#an meman#un ru"e $ sa+a an hal "erseu" "ia) seanin# en#an ea a)"u "em*uh yan# ia*a". !al ini a*a" iliha" ari *an+an# +alan yan# a)an ian#un.

8. Den#an *eruahan eman an su**ly

c. $ o1erlay sehin##a ITP men+ai &.$

(21)

PA

=

100

x

60000

=

60000

orang

=

30000

kendaraan

AB

=

30000

_orang

=

15000

_kendaraan

Searan *er#era)an ian##a* men#i)u"i hu)um gravity sea#ai eri)u". Q_AB= P_A x A_B T _Q AB x k

Q

_AB

=

30000

x

15000

T

_Q AB

x

0.0025 Q_AB= 1125000 T _Q AB

T

_Q AB

=

T

_o

[

1

−(

1

−

_a

)

Q

C

1

−

Q

C

]

!uun#an an"ara a)"u "em*uh en#an 1olume arus lalu lin"as un"u) ru"e $ ia*a" se*er"i eri)u".

T

_Q 1

=

25

[

1

−(

1

−

0.1

)

Q

7000 1

−

Q

7000

]

T

_Q₁

=

25

[

7000

−(

0.9

)

Q

7000

−

_Q

]

(22)

T

_Q 2

=

40

[

1

−(

1

−

0.9

)

Q

3000 1

−

Q

3000

]

T

_Q 2

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

• u"e $ 1125000

Q

1

=

25

[

7000

−(

0.9

)

Q

7000

−

_Q

]

1125000

Q

1

=

[

175000

−

22.5

Q

1 7000

−

_Q

₁

]

787500

_x

104

−

1125000

_Q

₁

=

175000

_Q

₁

−

22.5

_Q

₁2 22.5

_Q

₁2

−

1300000

_Q

₁

+

787500

_x

104

=

0

Q

1 1

=

50901.791

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

1 2

=

6875.985

kendaraan

jam

… … … …

(

memenuhi

)

(23)

T

_Q AB

=

1125000

Q

_AB

T

_Q AB

=

1125000 6875.985

=

163.612

menit

• u"e 2 1125000

Q

2

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

1125000

Q

2

=

[

120000

−

4

Q

2 3000

−

_Q

₂

]

3375

_x

106

−

1125000

_Q

₁

=

120000

_Q

₂

−

4

_Q

₂2 4

_Q

₂2

−

1245000

_Q

₂

+

3375

_x

106

=

0

Q

2 1

=

308515.126

kendaraan

jam

… … … …

(

tidak memenuhi

)

Q

2 2

=

2734.874

kendaraan

jam

… … … …

(

memenuhi

)

T

_Q AB

=

1125000

Q

_AB

T

_Q AB

=

1125000

2734.874

=

411.353

menit

Syarat batas

(

1

)

:

_Q

AB

=

Q

1

+

Q

2

Syarat batas

(

2

)

:

_T

(24)

[

175000

−

22.5

_Q

₁ 7000

−

_Q

₁

]

=

[

120000

−

4

_Q

₂ 3000

−

_Q

₂

]

52500

_x

104

−

67500

_Q

₁

−

175000

_Q

₂

+

22.5

_Q

₁

_Q

₂

=

84000

_x

104

−

14000

_Q

₂

−

120000

_Q

₁

+

4

_Q

₁

_Q

₂ 52500

_Q

₁

+

18.5

_Q

₁

_Q

₂

=

31500

_x

104

+

161000

_Q

₂

Q

1

(

52500

+

18.5

Q

2

)=

31500

x

10 4

+

161000

_Q

₂

Q

1

=

31500

_x

104

+

161000

_Q

₂ 52500

+

18.5

_Q

₂

T

_Q AB

=

1125000

Q

1

+

Q

2 1125000

Q

1

+

Q

2

=

120000

−

4

Q

2 3000

−

_Q

₂ 1125000 31500

_x

104

+

161000

_Q

₂ 52500

+

18.5

_Q

₂

+

Q

2

=

120000

−

4

Q

2 3000

−

_Q

₂ 1125000 31500

_x

104

+

161000

_Q

₂

+

_Q

₂

(

52500

+

18.5

_Q

₂

)

52500

+

18.5

_Q

₂

=

120000

−

4

Q

2 3000

−

_Q

₂ 1125000 31500

_x

104

+

161000

_Q

₂

+

52500

_Q

₂

+

18.5

_Q

₂2 52500

+

18.5

_Q

₂

=

120000

−

4

Q

2 3000

−

_Q

₂ 1125000

(

52500

+

18.5

_Q

₂

)

31500

_x

104

+

161000

_Q

₂

+

52500

_Q

₂

+

18.5

_Q

₂2

=

120000

−

4

_Q

₂ 3000

−

_Q

₂

(25)

5.906

_x

1010

+

20812500

_Q

₂ 31500

_x

104

+

213500

_Q

₂

+

18.5

_Q

₂2

=

120000

−

4

_Q

₂ 3000

−

_Q

₂

Q

2 1

=

300632.1269

kendaraan

jam

… … … …

(

tidakmemenuhi

)

Q

2 2

=

2083.858

kendaraan

jam

… … … …

(

memenuhi

)

Q

2 3

=−

3006.526

kendaraan

jam

… … … …

(

tidakmemenuhi

)

Q1= 31500 x104₊161000Q2 52500₊18.5_Q₂ Q1

=

31500_x104

+

161000

(

2083.858

)

52500

+

18.5

(

2083.858

)

Q

1

=

31500

_x

104

+

335501138 52500

+

38551.373

Q

1

=

650501138 91051.373

=

7144.33

kendaraan

jam

T

_Q AB

=

1125000

Q

1

+

Q

2

T

_Q AB

=

1125000

(26)

$ 6875.985 ₀ 163.612

2 0 2734.874 411.353

$>2 7144.33 2083.858 121.909

-erasar)an hasil yan# ia"as ia*a")an aha ru"e yan# i*ilih aalah ru"e $. Da*a" iliha" aha a)"u "em*uh ru"e $>2 leih ce*a" ianin#)an en#an ru"e $. ?amun, arus lalu lin"as un"u) ru"e $ un"u) *en#o*erasian )eua ru"e "elah meleihi )a*asi"asnya. !al "erseu" a*a" menyea)an )emace"an *aa ru"e $. Selain i"u, iaya yan# i)eluar)an un"u) meman#un ru"e $>2 a)an leih mahal

ianin#)an en#an meman#un ru"e $ sa+a an hal "erseu" "ia) seanin# en#an ea a)"u "em*uh yan# ia*a". !al ini a*a" iliha" ari *an+an# +alan yan# a)an ian#un.

Metode G#a$!"

$. a. (i)a hanya ruas $ yan# ero*erasi, era*a arus yan# "er+ai an"ara A an - an era*a a)"u "em*uhnya/

. (i)a hanya ruas 2 yan# ero*erasi, era*a arus yan# "er+ai an"ara A an - an era*a a)"u "em*uhnya/

c. (i)a hanya ruas $ an ruas 2 ero*erasi ersama0sama, era*a arus yan# "er+ai an"ara A an -, an era*a a)"u "em*uhnya/

. (i)a hanya ruas 5 sa+a yan# ero*erasi, era*a arus yan# "er+ai an"ara A an -, an era*a a)"u "em*uhnya/

e. Tolon# ie1aluasi mana yan# ana *ilih $, 2, $ an 2, a"au 5 f. -a#aimana +i)a $, 2, 5 ero*erasi ersama0sama

2. Asumsi)an "er+ai *enin#)a"an. !i"un# *oin a0f

. $ ilear)an sehin##a )a*asi"as men+ai 6&&& )en7+am 8. Den#an *eruahan demand an supply

(27)

. $ ilear)an sehin##a )a*asi"as men+ai 6&&& )en7+am

$. -eri)u" rumus0rumus yan# i#una)an alam *en#er+aan soal.

PA

=

90

100

x

60000

=

54000

orang

=

27000

kendaraan

AB

=

25000_orang

=

12500_kendaraan

Q

_AB

=

27000

x

12500

T

Q AB

x

0.0025 Q_AB= 843750 T _Q AB

T

_Q₁

=

25

[

5000

−(

0.6

)

Q

5000

−

_Q

]

T

_Q₂

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

T

_Q₃

=

15

[

6000

−(

0.8

)

Q

6 000

−

_Q

]

(28)

a. u"e $

. u"e 2

(29)

. u"e 5

(30)

(31)

-erasar)an hasil yan# ia"as ia*a")an aha ru"e yan# i*ilih aalah ru"e $>2>5. Da*a" iliha" aha a)"u "em*uh ru"e $>2>5 *alin# ce*a" ianin#)an en#an yan# lain. @alau*un iaya yan#

i)eluar)an un"u) meman#un ru"e $>2>5 a)an leih mahal ianin#)an en#an meman#un ru"e $>2, namun hal "erseu" seanin# en#an ea a)"u "em*uh yan# ia*a". Un"u) masalah iaya yan# i)eluar)an a*a" iliha" ari *an+an# +alan yan# a)an ian#un.

2. Asumsi "er+ai *enin#)a"an

(32)

PA

=

100

x

60000

=

60000

orang

=

30000

kendaraan

AB

=

30000

_orang

=

15000

_kendaraan

Q

_AB

=

P

A

x A

B

T

_Q AB

x k

Q_AB= 30000_x15000 T _Q AB x 0.0025

Q

_AB

=

1125000

T

Q AB

T

_Q 1

=

25

[

5000

−(

0.6

)

Q

5000

−

_Q

]

T

_Q 2

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

T

_Q 3

=

15

[

6000

−(

0.8

)

Q

6000

−

_Q

]

(33)

a. u"e $

. u"e 2

(34)

. u"e 5

(35)

(36)

-erasar)an hasil yan# ia"as ia*a")an aha ru"e yan# i*ilih aalah ru"e $>2>5. Da*a" iliha" aha a)"u "em*uh ru"e $>2>5 *alin# ce*a" ianin#)an en#an yan# lain. @alau*un iaya yan#

i)eluar)an un"u) meman#un ru"e $>2>5 a)an leih mahal ianin#)an en#an meman#un ru"e $>2, namun hal "erseu" seanin# en#an ea a)"u "em*uh yan# ia*a". Un"u) masalah iaya yan# i)eluar)an a*a" iliha" ari *an+an# +alan yan# a)an ian#un.

. $ ilear)an sehin##a )a*asi"as men+ai 6&&& )en7+am

(37)

PA

=

90

100

x

60000

=

54000

orang

=

27000

kendaraan

AB

=

25000

_orang

=

12500

_kendaraan

Q

_AB

=

P

A

x A

B

T

_Q AB

x k

Q_AB= 27000_x12500 T _Q AB x 0.0025

Q

_AB

=

843750

T

Q AB

T

_Q₁

=

25

[

7000

−(

0.9

)

Q

7000

−

_Q

]

T

_Q 2

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

T

_Q₃

=

15

[

6000

−(

0.8

)

Q

6000

−

_Q

]

Den#an men##una)an rumus yan# ia"as ma)a ia*a")an hasil se*er"i eri)u" ini. a. u"e $

(38)

. u"e 2

(39)

. u"e 5

(40)

(41)

-erasar)an hasil yan# ia"as ia*a")an aha ru"e yan# i*ilih aalah ru"e $. Da*a" iliha" aha a)"u "em*uh ru"e $>2>5 *alin# ce*a" ianin#)an en#an yan# lain. ?amun i)arena)an iaya yan# i)eluar)an un"u) meman#un ru"e $>2>5 a)an +auh leih mahal ianin#)an en#an *eman#unan ru"e $an a)"u "em*uh yan# ia*a" "ia) "erlalu +auh ma)a ru"e yan# i*ilih aalah ru"e $. Un"u) masalah iaya yan# i)eluar)an a*a" iliha" ari *an+an# +alan yan# a)an ian#un.

8. Den#an *eruahan eman an su**ly

. $ ilear)an sehin##a )a*asi"as men+ai 6&&& )en7+am -eri)u" rumus0rumus yan# i#una)an alam *en#er+aan soal.

PA

=

100

x

60000

=

60000

orang

=

30000

kendaraan

AB

=

30000_orang

=

15000_kendaraan

Q

_AB

=

30000

x

15000

T

Q AB

x

0.0025 Q_AB=1125000 T _Q AB

T

_Q 1

=

25

[

7000

−(

0.9

)

Q

7000

−

_Q

]

(42)

T

_Q₂

=

40

[

3000

−(

0.1

)

Q

3000

−

_Q

]

T

_Q₃

=

15

[

6000

−(

0.8

)

Q

6000

−

_Q

]

Den#an men##una)an rumus yan# ia"as ma)a ia*a")an hasil se*er"i eri)u" ini. a. u"e $

(43)

c. u"e $>2

(44)

(45)

-erasar)an a"a yan# ia"as ia*a")an #rafi) se*er"i eri)u" ini