[123doc.vn] bai tap van tai co loi giai

7/23/2019 [123doc.vn] Bai Tap Van Tai Co Loi Giai

1/8

Bai tap Van tai co li giai

Bai 1 Cho bai toan van tai:

A = (33, 39, 12)

B = (15, 15, 19, 21, 14)

C =

8 11 7 6 10

6 12 12 5 125 14 7 8 15

1) Giai bai toan tren.

2) Phng an toi u co duy nhat khong, tai sao?

ay la bai toan can bang thu phat. Dung phng phap chi ph thap nhat e thanh lap phng ancc bien xuat phat roi giai tiep, ta co cac bang van tai sau:

8

0

11 (3)

+7

19

6 (1) 10

14

-8

6

+3

12

15

12 5

21

12

-6

5

12

14 7 8 15

-5

0 6 -1 -1 2 B.1

Tai bang 1 th o= 0 nen phng an cc bien tai bang 2 cung chnh la phng an cc bien tai bang

1. Lu y rang, trong bang 2 th o (r, s), tc la o (1, 2), se tr thanh o chon con o (g, h), tc la o (1, 1)

se tr thanh o loai:

8 11

+0

7

19

6 10

14

0

6

+3

12

15

12 5

21

12

-1

5

12

14 7 *+

8 15

0

5 11 7 4 10 B.2

Tai bang 2 th ij0 (i, j) nen phng an cc bien ang xet la phng an toi u. Ta co:

Xmin=

0 0 19 0 14

3 15 0 21 0

12 0 0 0 0

vi zmin= 636

2) V o (3, 3) la o loai va 33= 0 nen ta xem o (3, 3) la o (r, s), them o nay vao tap o chon va o chon

gia, tm vong, lap bang 3:


2/8

8 11

12

7

7

6 10

14

0

6

15

12

3

12 5

21

12

-1

5 14 7

12

8 15

0

5 11 7 4 10 B.3

Do o giam ham muc tieu t bang 2 xuong bang 3 la ors= 0 nen phng an cc bien tai bang 3

cung la phng an toi u:

Xmin=

0 12 7 0 14

15 3 0 21 0

0 0 12 0 0

Phng an toi u Xminkhac phng an toi u Xmintai bang 2. Vay, bai toan khong duy nhat phng

an toi u.

Bai 2 Giai bai toan van tai:

A = (39, 12, 20)

B = (24, 33, 62)

C =

4 3 6

5 2 7

8 3 5

Do 39+12+20=71 < 24+33+62=119 nen ay la bai toan van tai ma kho co t hang hn. Ta lap them

mot kho gia co lng hang b thieu la 11971 = 48. Chi ph van chuyen mot n v hang t kho gia

ra moi ca hang eu bang 0.

Luc nay ta co bai toan can bang thu phat. Dung phng phap chi ph thap nhat e thanh lap

phng an cc bien xuat phat roi giai tiep, ta co cac bang van tai sau:

4

+18

3

21

6

-4

5 2

12

7

-3

8 3 (1) + 5 20

-5

0

6

0 0

+42

0

0 -1 0 B.1


3/8

4

24

3

15

6

-3

5 2

12

7

-2

8 3

6

5

14

-3

0 0 0

48

2

1 0 2 B.2

Tai bang 2 th ij0 (i, j) nen phng an cc bien ang xet la phng an toi u. Bo i kho gia, ta

co:

Xmin=

24 15 0

0 12 0

0 6 14

vi zmin= 253

Bai 3 Giai bai toan van tai sau ay vi yeu cau ca hang th 2 va th 4 nhan u hang:

A = (15, 25, 35)

B = (10, 20, 30, 60)

C =

1 3 6 9

6 8 2 7

3 9 3 6

Do kho t hang hn nen ta them mot kho gia (kho th 4) co lng hang chenh lech la 45. Theo ieu

kien ca hang th 2 va th 4 nhan u hang nen o (4, 2) va (4, 4) la o cam. Vay, ta ieu chnh c 42va

c44thanh M (M la so dng u ln).

Luc nay ta co bai toan can bang thu phat. Dung phng phap chi ph thap nhat e thanh lap

phng an cc bien xuat phat roi giai tiep, ta co cac bang van tai sau:

1 3

+15

6 9

0-9

6 8 2 7

25 -7

3 9 3 6

35

-6

0

10

M

5

0

30

M (6)

+ -M-6

-M-6 -6 -M-6 0 B.1


4/8

1 3

15

6 9

M-3

6 8 2 7

25

M-7

3 9 3 6

35

M-6

0

10

M

5

0

30

M

0

0

0 M 0 M B.2

Tai bang 2 th ij0 (i, j) nen phng an cc bien ang xet la phng an toi u cua bai toan M. Do

phai phan phoi hang vao o cam (4, 2) nen bai toan co o cam vo nghiem do khong co phng an.

Bai 4 Hay lap mo hnh toan cua bai toan sau (khong yeu cau giai):

Ngi ta can trong 4 giong lua tren 3 tha ruong. Do ac iem cua moi giong lua va moi tha ruong

la khac nhau nen chi ph trong lua tren 1 ha la khac nhau va c cho bi bang:

Giong lua

Tha ruongL1 L2 L3 L4

R1 2 3 2 3

R2 3 3 2

R3 1 4 3

c biet, dien tch moi tha ruong lan lt la 30ha, 60ha va 45ha con tong dien tch can trong moi

giong lua lan lt la 28ha, 12ha, 10ha va 20ha. Ngoai ra, ngi ta cung biet rang tren tha ruong 2

khong trong c giong lua th 3, tren tha ruong 3 khong trong c giong lua 4.

Hay cho biet phai phan phoi at trong nh the nao e tong chi ph la thap nhat.

Quan niem moi tha ruong la mot tram phat va dien tch tha ruong la lng hang co tai tram

phat, ta co A = (30, 60, 45).

Quan niem moi giong lua la mot tram thu va dien tch can trong la lng hang ma tram thu can

nhan, ta co B = (28, 12, 10, 20).

T bang chi ph trong cac giong lua ta co ma tran C.

Do tha ruong 2 khong trong c giong lua th 3 va tren tha ruong 3 khong trong c giong lua

4 nen o (2, 3) va (3, 4) la o cam. Ta gan c23= M, c34= M vi M la mot so dng u ln.

Goi xij la so ha at tren tha ruong th i dung e trong giong lua th j. Ta co xij 0

(i 1,3; j 1,4)= = .

Vay, bai toan tren co mo hnh toan la bai toan van tai co o cam sau:

A = (30, 60, 45)

B = (28, 12, 10, 20)

C =

2 3 2 3

3 3 M 2

1 4 3 M

Bai 5 Mot doanh nghiep can mua go cho cac xng san xuat ban ghe t mot so a phng. Nhu cau gocho nha may at tai Bnh Dng la 250m3, tai quan 12 la 125m3, tai Thu c la 100m3. Hien nay

trai go tai Di Linh ang ban 300 m3go, tai ac Lac ang ban 80m3go va tai Kontum ang ban120m3go. c biet gia go tai Di Linh la thap nhat con tai ac Lac va Kontum la cao ngang nhau.

Ph van chuyen (chuc ngan/m3) cho bi bang:


5/8

Xng tai

Bnh Dng

Xng tai

quan 2Xng tai

Thu c

Trai go Di Linh 20 40 35

Trai go ac Lac 15 45 40

Trai go Kontum 18 50 45

Hay tm cach mua go va van chuyen sao cho tong chi ph van chuyen la thap nhat.

Quan niem moi trai go la mot tram phat va so m3go ang ban la lng hang co tai tram phat, ta coA = (300, 80, 120).

Quan niem moi xng la mot tram thu va nhu cau go cua moi xng la lng hang ma tram thu can

nhan, ta co B = (250, 125, 100).

T bang chi ph van chuyen ta co ma tran C.

Do gia go tai Di Linh thap nhat nen doanh nghiep se u tien mua het go tai Di Linh. Vay, yeu cau

cua bai toan la tram phat 1 phai phat het hang.

Goi xijla so m3go ch t tram phat th i ve tram thu th j. Ta co xij0 (i 1,3; j 1,4)= = .

Vay, bai toan tren co mo hnh toan la bai toan van tai sau ay vi yeu cau tram phat 1 phai phathet:

A = (300, 80, 120)

B = (250, 125, 100)

C =

20 40 35

15 45 40

18 50 45

Do tram phat nhieu hang hn nen ta them mot tram thu gia (tram thu th 4) nhan lng hang

chenh lech la 25. Theo yeu cau tram phat 1 phat het hang nen o (1, 4) se la o cam. Vay, ta ieu

chnh c14thanh M (M la so dng u ln).

Luc nay ta co bai toan van tai can bang thu phat. Dung phng phap chi ph thap nhat e thanh

lap phng an cc bien xuat phat. Theo cach giai a biet, ta co:

Xmin=

75 125 100 0

80 0 0 0

95 0 0 25

vi zmin= 12.910

Vay ke hoach mua go toi u la:

Mua tai Di Linh 75m3go, tai ac Lac 80m3go, tai Kontum 95m3go e cung cap xng san

xuat tai Bnh Dng.Mua tai Di Linh 125m3go cho xng san xuat tai quan 2.

Mua tai Di Linh 100m3go cho nha xng san xuat tai quan Thu c.

Tong chi ph van chuyen thap nhat la 129 trieu 1 tram ngan ong.

Bai 6 Mot x nghiep may co 50 th tay nghe cap 1, 30 th tay nghe cap 2 va 40 th tay nghe cap 3 ngmay ao tren 40 may may loai 1, 60 may may loai 2, 20 may may loai 3. Nang suat (so lng ao/gi)

cua moi ngi th thuoc mot cap tay nghe khi s dung mot loai may may cho bi bang sau:

May may

loai 1 loai 2 loai 3

Th cap 1 7 8 9

Th cap 2 6 7 8

Th cap 3 4 6 7

Tm cach phan cong th sao cho tong nang suat la cao nhat.


6/8

Quan niem moi cap th la mot tram phat va so th la lng hang co tai tram phat, ta co A = (50,

30, 40).

Quan niem moi loai may may la mot tram thu va so th ng may la lng hang ma tram thu cannhan, ta co B = (40, 60, 20).

T bang nang suat ta co ma tran C.

Goi xij la so th co tay nghe cap i c phan cong ng tren may may loai j. Ta co x ij 0

(i 1,3; j 1,3)= = (bo qua ieu kien nguyen).

Vay, bai toan tren co mo hnh toan la bai toan van tai max sau ay:

A = (50, 30, 40)

B = (40, 60, 20)

C =

7 8 9

6 7 8

4 6 7

Theo cach giai a biet, ta tm c phng an toi u cua bai toan tren la:

Xmax=30 0 2010 20 0

0 40 0

vi zmax= 830

Vay, cach phan cong th toi u la:

Phan cong 30 th tay nghe cap 1 ng may tren 30 may may loai 1.





Vi cach phan cong nay th nang suat se at toi a va bang 830 ao trong 1 gi.

Bai tap Van tai

GIAI BAI TOAN VAN TAI

Bai 1 Giai bai toan van tai sau:

A = (218, 210, 105, 12)

B = (123, 142, 115, 165)

C =

12 65 74 28

16 67 72 33

17 63 73 29

18 68 77 30

Bai 2 Cho bai toan van tai:

A = (50, 40, 20)

B = (40, 30, 20, 20)

C =

5 1 3 4

1 2 1 3

3 4 5 6

Giai bai toan va cho biet phng an toi u co duy nhat khong, tai sao?


7/8

Bai 3 Cho bai toan van tai max sau:

A = (50, 30, 40)

B = (40, 60, 20)

C =

7 8 9

6 7 8

4 6 7

Giai bai toan va cho biet phng an toi u co duy nhat khong, tai sao?

Bai 4 Cho bai toan van tai sau:

A = (40, 50, 60)

B = (25, 35, 45)

C =

7 8 6

2 7 8

9 6 7

Giai bai toan tren vi yeu cau la kho 1 phai phat het va kho 2 khong c phat vao ca hang 3.

Bai 5 Cho bai toan van tai sau:

A = (40, 50)

B = (25, 35, 30)

C =7 8 6

2 7 8

1) Viet bai toan tren thanh bai toan QHTT. Bai toan co bao nhieu bien, bao nhieu rang buoc?

2) Viet bai toan oi ngau cua bai toan QHTT tren vi ky hieu bien la u1, u2, v1, v2, v3.

3) Phat bieu nh ly o lech bu yeu vi cap bai toan oi ngau tren.Bai 6 Cho bai toan van tai sau:

A = (40, 65)

B = (25, 35, 40)

C =7 8 6

2 7 8

Vi yeu cau kho 1 phai phat het hang, hay viet bai toan tren thanh bai toan QHTT.

LAP MO HNH (khong yeu cau giai)

Bai 7 ai hoi the van dien ra cung ngay tai 4 a iem. Ngi ta can ch en cac mot so thiet b t 3 nicung cap. Cac d lieu ve lng hang can chuyen ch va khoang cach gia cac a iem c cho bi

bang:

Thu

Phat15 10 17 18

20 160 50 100 70

23 100 200 30 120

10 50 40 30 50

Do ac iem cua cac phng tien van chuyen va yeu cau ve thi gian nen khong the ch hang i xaqua 150Km.

Tm phng an van chuyen toi u.


8/8

Bai 8 Mot ca hang ban gao can phan phoi gao t 3 kho en 4 ai ly. So bao gao co trong moi kho va sobao gao ma moi ai ly co the nhan cho bi bang:

Thu

Phat170 150 210 160

120 4 1 1 2

230 5 4 2 3

310 6 2 3 1

c biet, ai ly I yeu cau c nhan khong di 145 bao gao. Lap ke hoach phan phoi toi u.

LAP MO HNH VA GIAI

Bai 9 Cong ty trang trai Cao Nguyen d nh trong 02 loai cay ca phe & tieu tren 3 khu at A, B, C codien tch tng ng la: 50, 60, 40 (ha). Do ac iem cua cac khu at khac nhau nen chi ph san xuat

(trieu ong/ha) va nang suat (ta/ha) khac nhau va cho bang sau:

Khu at Ca phe Tieu

A2

9

1,8

6

B2,2

10

1,6

5

C2,5

12

1,5

4

(So lieu goc ben trai, pha tren cua moi o la chi ph SX; goc ben phai pha di cua moi o la

nang suat)

Yeu cau san lng cua ca phe toi thieu la 500 ta va tieu toi thieu la 420 ta.

Hay xac nh phng an phan phoi at trong sao cho am bao yeu cau ve san lng vi chi ph thap

nhat.

Bai 10 Mot cong ty xay dng muon mua sat e xay dng cac khu nha tai quan 2, quan Thu c, quan BnhThanh t cac nha may Luyen can thep tai Bien Hoa, Bnh Dng va quan Tan Bnh. Nhu cau sat

xay khu nha tai quan 2 la 1250 tan, tai Thu c la 500 tan va tai Bnh Thanh la 650 tan. Cong ty

mua c tai Nha may thep Bien Hoa 800 tan, tai Bnh Dng mua c 900 tan va tai Tan Bnh

mua c 1200 tan. Ph van chuyen (tan/chuc ngan) cho bi bang sau:

Khu nha q.2 Khu nha Thu c Khu nha Bnh ThanhNha may tai Bien Hoa 3 2 8

Nha may tai Bnh Dng 7 6 12Nha may tai Tan Bnh 4 5 3

Biet rang hien nay khong the ch sat t quan Tan Bnh ve quan 2. Lap phng an van chuyen sat

sao cho cac khu xay dng nhan u sat va tong chi ph van chuyen la thap nhat.

Bai 11 Mot trang trai co 3 manh at nh dung e trong 4 loai cay. Li nhuan thu c khi trong moi loaicay tren moi loai at, dien tch moi manh at, dien tch nh trong moi loai cay cho bi bang sau.

Lap ke hoach phan phoi at trong sao cho tong li nhuan thu c la ln nhat, biet rang tren manh

at th 2 khong c trong loai cay th 2.

Li nhuan (n v tien/ha)

Loai cay 1 Loai cay 2 Loai cay 3 Loai cay 4

Dien tch

manh at (ha)

Manh at 1 22 25 20 18 250

Manh at 2 30 32 25 28 1.400

Manh at 3 29 28 25 23 350Tong dien tch

trong (ha)500 400 600 500

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