Bai Tap Toan Kinh Te Them 7682

8/2/2019 Bai Tap Toan Kinh Te Them 7682

1/20

BI TP TON KINHT

CHNG I: QUY HOCH TUY N TNH

I.

Lp m hnh ton hc cho cc bi ton d i

y1.Mt x nghip c 4 my A, B,C, D dng sn xut ra 6 loi sn phm nh mcthi gian cho mi sn phm i vi tng my, qu thi gian ca tng my c cho trong

bng sau:SP

MYnh mc thi gian cho sn phm ( gi)

SP1 SP2 SP3 SP4 SP5 SP6A: 132 1 2 1 3 1 0B: 120 2 1 1 2 3 2C: 100 1 2 0 2 1 3

D: 144 2 2 2 1 4 2Gi 1 SP(1000 )

40 30 35 75 65 60

Hy lp phng n sn xut sao cho tng thu nhp l ln nht (Max) m vn m bo anton cho my.

2. Mt phn xng c nhim v sn xut ra 3 loi sn phm cn s dng 2 loinguyn liu A v B. Hao ph nguyn liu, d tr nguyn liu cho trong bng di y.Hy lp k hoch sao cho tng chi ph nh nht vi iu kin khng c s dng qu snguyn liu, tng s sn phm c 3 loi khng t hn 350 s sn phm 1, khng t hn25% tng s sn phm.Nguyn liu Sn phm D tnh nguyn liu

(kg)I II IIIA 2 1 3 1500B 1 2 2 650

Chi ph/ SP(1000)

8 5 10

3. Hai a phng Ninh Bnh v Hng Yn cung cp Khoai vi khi lng 200 tnv 300 tn cho 3 a phng tiu th Khoai l Hi Phng, Ngh An v Nam nh vi yucu tng ng l 170 tn, 200 tn v 130tn cc ph (nghn/ tn) cho trong bng diy. Hy lp k hoch sao cho tng chi ph nh nht.

Ni tiu thHi Phng Ng An Nam nh

Ninh Bnh 20 12 25Hng Yn 12 24 14

B mn Ton - Bi tp Ton Kinh T - Dng cho SV cc lp tn ch! 1


2/20

1 2

4. Ba khu t ngi ta d tnh trng 3 lo cy lng thc: Ng, khoai v sn. Nngsut v chi ph trn 1ha vi mi loi cy tng khu t v nng sut (t) chi ph1000/ha.Din tch(ha) Ng Khoai SnKI:30 150 80 80KII:50 120 75 90

KIII:27 140 70 70Yu cu 1000 1200 1500Hy phn b cy trng cho ht t ai sao cho m bo yu cu v s lng v tng chi

ph l nh nht.5. C 2 x nghip sn xut 2 loi sn phm. Bit rng u t 1000 vo x nghip I

trong 1 n v thi gian lm c 1,2 sn phm A v 1,8 sn phm B cn u t 1000vo x nghip II lm c 1,8 SP A v 0,8 Sp B. Nguyn liu v lao ng cung cp chovic sn xut, nh mc nguyn liu lao ng v d tr nguyn liu cho trong bng diy.Hy tm phng n u t sao cho tng s vn b ra t nht.

Nguyn liu d tr: 400 tn v gio lao ng l 200000 giXN nh mc hao ph LN(kg/SP), lao ng(gi/SP)

A BNL L NL L

I 4 2 10 4II 4,2 3 9 4,5

Yu cu slng SP

21000 20000

II .Giicc bi ton sau bng phng php hnh hc 2x1 +x2

8

2x +x 10

1. f(X) = x1+x2Min

tha mn x1

x2 4

2

x1+

x2

4

x1 ,x2 0

x1 +x2 2

3x1 2x2 6

2. f(X) =6x1

+ 5x2Max

tha mn x1+

2x 1

x2 2

x2 0

x1 ,x2 0


3/20



4/20

1 2

1 2

1

1

3

3. Max ( x1 - x2 ) tha mn

2x1 3x2 62x +x 6

x1 2x2 1

x1 + x2 5

x1 ,x2 0

x1 2x2 0 x +2x 6

4. Min ( 4x1 + x2 ) tha mn 3x1 +x2 62x +x 4 1 2

x1 ,x2 0

III. Gii cc bi ton sau bng phng php n hnh

Bi1.

f(X) = x1 x2 +x3 +x4 +x5 x6Min

x1

3x1 +x2 4x

3

+x4 + 6x6 = 9

+ 2x6 = 2

x + 2x +x5 + 2x6 = 2

x j 0 ; j = 1, 6

Bi2.

f(X) = 5x1 + 2x2 + 4x3 +x4 + 5x5 + 3x6Min

2x1 +x2 +4x3

+ 3x5 = 152

4x1

3x

+ 2x3 +x4 + 3x5+x5

= 60

+x6 = 36

x j

0,

j = 1, 6


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Bi3.

f(X) = 4x2 2x3 13x4 +7x5 + 10x6Min

x1 3x2 + 2x3 + 13x4 7x5 12x6

x2+x

3+ 4x

4x

54x

6

= 9

= 3

2x2 +x3 2x4 + 2x5 4x6 = 9

x j 0,

j = 1, 6

Bi

4.

f(X) = x1 +x2 x3Max



6/20

2x1 +x2 + 3x3 +x4 = 1

x1

+ 2x2 2x3

x j 0

+x5 = 1

j = 1, 5

Bi5.

f(X) = 3x1 + 2x2 + 14x3 + 13x4 + 4x5Max

x1

+ 2x3 +x4 +x5 = 1

x2 +x3 x j

0

+ 2x4 +x5 = 1

j = 1, 5

Bi6.

f(X) = 2x1 +x2 + 5x3 + 3x4Min

x1 + 2x2 +3x3

= 15

2x1 +x2 + 5x3 = 20

x1 + 2x2 +x3 +x4 = 10

x j 0

j = 1, 4

Bi7.

f(X) = 2x1 + 8x2 + 2x3Max

4x1 x2 +

3x3 7x1 + 5x2 +

12x3

= 7

= 19

x j 0 j = 1, 3


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1

Bi8.

f(X) = 3x1 + 7x2 + 6x3 + 5x4Max

x1 + 2x2 + 5x3 +

3x4 4x1 + 3x2 + 2x3 x4

= 12

= 7

x j 0 j = 1, 4

Bi9.

f(X) = x1 +x2 + 2x3 2x4 4x5Min

x1 +x2 3x3 + 2x4 2x5 = 8 2x1 x

3 +x4 x5 21

3x1 + 5x3 3x4 + 2x5 = 25

2x x j

0

+x4 + 4x5

j = 1, 5

20



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1

2

Bi10.

f(X) = 2x1 + 3x2 x3 4x4 + 6x5Max

2x1 +x2 x3

= 40

5x1 x1

2x3+ 2x3

+ 2x44x4

x5 0

+x5 12

3x

+ 2x3 + x4 + 2x5 14

x j 0 j = 1, 5

Bi11.

f(X) = 2x1 +x2 3x3 +x4Min

2x1 +x2 +

4x3

+x4 = 6

5x1 + 2x2 + 2x3 +

x4

= 10

x j 0 j = 1, 4

Bi12.

f(X) = 2x1 +x2 + 3x3 x4Min

x1 2x2 +x4 = 16

x2 +x3 4x4 8

x x j 0

+ 3x3 2x4

j = 1, 4

20

Bi13.

f(X) = 2x1 + 4x2 +x3 +x4Max

x1 + 3x2


9/20

+x4 1 2x1 +

x2 3

x2 + 4x3 +x4 3

x j 0 j = 1, 4

Bi14.

f(X) = 2x1 + 4x2 +x3 +x4Max

x1 + 3x2 +x4 1

2x1 +

x2 3

x2 + 4x3 +x4 3

x j 0 j = 1, 4

Bi15.

f(X) = 2x1 + 5x2 +x3 2x4Max



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1

1

2

2

3x1+ 2x3 5x4 23

4x1

+x3 4x4 36

x2 2x3 + 2x4 = 14

2x +x3 3x4 12

x j 0 j = 1, 4

Bi16.

f(X) = x1 + 5x2 x3Min

x1 x2 + 4x3 + 3x4 8

3x1 5x2 + 2

x3

2x4 2

6x 4x3 5x4 2

x j 0 j = 1, 4

Bi17.

f(X) = 2x1 2x2 + 3x3 +x4 3x5Min

4x1

2x3+x

44x

5= 8

x1

+ 2x4 x56x3 +x4 + 3x5

20

= 15

x+x + x3 +x4 2x5 = 14

x j 0 j = 1, 5

a) Gii bi ton trn bng phng php n hnh.b) C th kt lun g trong trng hp f(X)Max

c) Tm phng n X sao cho


11/20

1 4

f(X)= 27

Bi 18. Cho bi ton vi tham s : f(X) = x1 +x3 x4Min

x1 +x2 +12x

3

2x4 + 4x5 = 9

2x1 + 8x3 + (1 )x4 +2x5

= 14

x + (1)x = 4

x j

0,

j = 1, 5

a) Bit x l mt phng n cc bin ng vi c s A1, A2, A5. Hy lp bng nhnh ng vi x .

b) T bng n hnh lp, hy tm tt c cc gi tr ca sao cho x l phng nti u.

c) Gii bi ton cho vi =1 v =3.

Bi 19. Cho bi ton vi tham s : f(X) = x2 3x4 +x5 + 6x6Min



12/20

2 4

x1 x2 +4x3

2x4 + 12x5 +11x6 = 9

2x2 + 2x3 + (1 )x4 + 8x5 +14

x6

= 14

x + (1)x + 3x6 = 4

x j

0,

j = 1, 6

1) Bit x l mt phng n cc bin ng vi c s A1, A2, A3. Hy lp bng nhnh ng vi x .

2) Tm tt c cc gi tr ca sao chox l phng n ti u.3) Gii bi ton cho vi =1 v =-1.

CHNG II: BI TON I NGU

Bi 1. Vit bi ton i ngu? Ch ra cc cp i ngu ca cc bi ton sau:

a) g(Y) = 7y1

+6y2

+4y3

Maxtho mn

y1 + 2y2 + 5y3 2 3y1

y2 +y3 3

2y13y2 + 2y3 4

y1 + 3y2 + 2y3 2

b) f(X) = 2x1 +x2 3x3 +x4Max

tho mn

2x1 +x2 +

3x3

+ 2x4 = 2

4x1 x2 + 2x3

x4 = 5

x j 0 j = 1,4

3x1 +x2 2x3 4


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4x1 x2 + 3x3 2 c) f(X) = 6x1 + 3x2 x3Min

tho mn 2x1 +x2

x3 4

x1 2x2 + 3x3 5

x j 0 j = 1, 3

4x1 x2 + 3x3 x4 22x1 + 3x2 x3 +2x4 5

x1 +x2 + 3x3 +x4 3

d) f(X) = 2x1 x2 + 3x3 4x4Max

tho mn 2x

x+ 2x x = 6

1 2 3 4

3x1 +x2 +4x3 +2x4 10x j 0 j = 1, 4



14/20

1

)

Bi 2. Cho biton

f(X) = x1 3x2 +x3 2x4

Min

tho mn

4x1 + 12

x2

+ 3x4 = 24

x1 + 3x2 x3 3

4x 18x2 + 2x3 + 3x4 33

x j 0

;

j = 1, 4

Chng minh rng x = (0;1;0; 4) l phng n ti u ca bi ton.

Bi 3. Cho biton

f(X) = 15x1 + 10x2 + 6x3

Min

tho mn

3x1x1

+2x3 2

+ 2x2 + 2x3 3

2x1 +x2 4x1 +2x2 x1

+x3 2

2x3 1

1

x2 0 , x3 0

Bit rng x = (1,5,

11l phng n ti u ca bi ton cho. Hy tm phong n ti u

4 4ca bi ton i ngu.

x1 +2x2 +x3 7

4x1 +3x2 6x3 9

2x1

x2

8x3

6

Bi 4. Cho biton

f(X) = x1 +x2 x3Max

tho mn

2x2 +x3 2


15/20

2x1 x2 + 5x3 1

a) Chng t rng cc phng n

x1

x = (4,6,1) ,y = (4,0,

3,0,

0,1)5 5

+ 3x3 1

x3 0

theo th t l

phng n ti u ca bi ton cho v bi ton i ngu ca n.b) Tm cc tp phng n ti u ca bi ton cho v bi ton i ngu ca n.



16/20

1

2 2

Bi 5. Cho biton

f(X) = x1 +x2 2x3 3x4 + 4x5

Min

tho mn

9x 2x +

3x 7

2 1 4 2 5 x + 4x +x

3x 42

1 2 4 5 2 1

x +x 1x = 5

2 3 5

x j 0 , j = 1, 5

a) Gii bi ton bng phng php n hnh.b) Tm li gii cho bi ton i ngu.Bi 6. Cho biton

f(X) = 4x1 4x2 + 2x3 3x4 2x5 2x6Max

tho mn

3x1 2x2 +x3 + 2x5 = 8

x1

+ 5x3 + 3x4 x5 = 3

5x1 4x3 +x5 +x6 = 5

x1,x3 ,x5

0

a) Vit bi ton i ngu, ch ra cp rng buc i ngu.b) Xc nh phng n ti u ca bi ton gc.

Bi7. Cho bi

tonf(X) = 5x

19x

2+ 5x

3+ 7x

4+ 3x

5Min

2x1 + 6x2 2x3

2x4 +x5 4

8x1 + 2x3 + 4x4 x5 = 20

x

x2

x j 0

+x3

j = 2,5

x5 1


17/20

(

a) Chng t rng phng n x = (0,1,0,5, 0) l phng n ti u ca bi ton cho.

Tm tp phng n ti u ca bi ton i ngu.b) Hy tm tt c cc phng n ti u ca bi ton cho c thnh phn

Bi 8. Cho bi ton vi tham s f(X) = 4x1 + 10x2 +2x3 8x4 + 9x5 +x6 4x7Min

x3= 4 .

2x1 +x3 2x4 + 2x5 6x7 = 7

2x1 2x2 + 2x3 + 4x4

3x5

+x6 = 7

4x1 + 3x2 2x3

2x4

+x5 +x6 22x7 = 20

x j 0

j = 1, 7

a) Tm gi tr ca x = 11

,0,0,9,0, 0,

3) l phng n ti u ca bi ton

cho.

2 2 2b) Trong trng hpx khng l phng n ti u, c th ni g v bi ton cho vbi ton i ngu ca n.



18/20

CHNG III: BI TON VN TI

Bi1.

Gii cc bi ton vn t i sau:

TP 20 50 50 2030 6 2 4 640 4 6 3 870 1 5 8 7

Bi 2.T

P50 90 90 70

110 7 8 5 3

110 2 4 5 980 6 4 1 2Bi 3.

TP

220 320 540 650

250 4 5 3 5790 7 5 4 9670 9 8 3 4340 7 6 6 2

Bi 4.T

P150 80 180 60 80

50 7 4 17 5 8200 7 15 10 11 30100 13 6 14 16 20200 14 22 17 16 35

Bi 5.T

P35 75 40 70 80

60 7 10 1 9 1285 9 4 10 11 548 8 7 5 6 8

107 10 7 3 13 9

Bi 6.



19/20

TP

40 80 75 50 55

60 8 6 4 5 775 7 3 9 6 1045 2 10 7 8 480 11 5 8 12 9

Bi 7.T

P35 15 65 25 40 20

70 4 7 7 10 11 630 10 5 2 3 8 960 12 6 4 11 9 740 13 5 11 6 7 5

Bi8.

TP

54 37 49 120 70

80 4 5 3 2 7120 7 5 3 4 M80 9 7 M 2 550 2 6 4 3 6

Bi 9.T

P

14 15 25 16 17 20 23

27 6 3 4 3 5 7 932 12 11 16 14 16 13 1743 5 6 4 7 4 5 628 7 9 10 11 9 6 9

Bi1.

CHNG IV: BI TON SN XUTNG B G ii cc bi ton ngbsau y:

Chi titMy

CT11

CT21

CT31

A:1 63 240 160B:1 103 61 200C:1 720 360 161D:1 173 120 240



20/20

Bi 2.Chi tit

MyCT1

1CT2

1CT3

1A:1 120 80 61B:1 36 100 91C:1 180 82 36

D:1 60 120 102Bi 3.

Chi titMy

CT12

CT21

CT33

CT42

A:1 76 50 105 80B:1 160 34 72 48C:1 180 36 108 60D:1 200 32 96 160

Bi 4.Chi tit

MyCT1

1CT2

1CT3

1CT4

1A:5 3 5 7 8B:4 8 6 6 6C:6 6 3 6 5D:8 5 2 4 10

Bi5.

Chi titMy

CT12

CT21

CT31

CT43

A:1 54 0 108 54B:5 96 32 14 15C:2 62 28 0 51D:1 242 128 96 192


Bai Tap Toan Kinh Te Them 7682

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