DAp AN DE THI HOC PHAN: MD HiNH ToAN KINH TE.Mii hoc phin: TOKT022 sa tin chi: 02Kh6a: _ Cao ding h~ Chinh quyNgay thi: / / SUdung tai lieu: Duoc0 Khong diroc [;]

Can Y NQidung Di~m

1 2d

NQi dung co ban cua phirong phap rna hinh trong nghien ciru va phan tich kinht€:a. D~t vdn d€: Chung ta c~n di~n dat ra vdn d€, hien nrong kinh t€ c~n quantam nghien CUu,muc dich la gi, cac nguon hrc co th~ huy dong d~ tham gianghien ciru.b. Mo hinh hoa:- Xac dinh cac y€u t6, sir kien c~n xem xet cung cac m6i lien h~ tnrc ti€p gifrachung rna ta co th~ cam nhan bang true quan hoac can ctr VaGco sa ly Iuan daIva chon.- Luong hoa cac yeu to nay, coi chung la cac bien cua rna hinh.- Xem xet vai tro cua cac bien s6 va thi€t l~p cac h~ thirc toan h9C - chu y€u lacac phuang trinh - rna ta quan h~ gifra cac bi€n.

0,25

0,25

0,25

c. Pharr tich rna hinh:- Sir d\lng phuang phap phan tich rna hinh d~ phan tich

0,25

0,25d. Giai thich ket qua:- Dva VaGk€t qua phan tich rno hinh ta se dua ra giili dap cho v~n d€ c~nnghien cUu.* Cho vi d\l dung, ra rang 0,25

* Neu dung bu&c d~t van de va rna hinh hoa 0,25

0,25* Neu dung bu&c phan tich va giai thich ket qua

2 5d

a 4d

- Vi rang bUQc1 co ve trai 16'0 han ho~c bang ve phai nen ta bat ve trai cua

rang bUQc1 mQt bi€n khong am x4•

0,25

- Vi rang bUQc3 co ve trai be han ho~c bang ve phai nen ta them ve trai cua

rang bUQc3 mQt bi€n khong am x5•- Vi rang bUQcbi€n co X2 :::;0 nen ta thay X2 bai -x2 trong toan bQbai toano

- Vi rang bUQcbi€n co X3 my y nen ta thay X3 bai X3 _ X6 trong tocin bQbcii 0,25

toano

0,25

TOAN_MHTKT_CDCQ_A-Q TRANG 1I4-MD: 060514676

--. ===============---==~~~==================~--

Dang chinh tilc cua bai toan dft cho la

13 2'f = --Xl -3X2 +2X3 - X6 ~ min3r+3x,- x, - 3x, ~ 2 0,25

(P') 2Xl +X2 +X3 -X6 = 4Xl - 2X3 + Xs + 2X6 = 5

-Xj :2: O,j = 1,6

_Vi rang buoc 1 chua co Anco ban nen ta them mQt Angia X7• 0,25

Dang chuan cua bai toan dft cho la

f = -~Xl -3x2 +2X3 -2X6 +MX7 ~ min3rl+3x,-x, -3x, +X, ~ 2 0,25

(PM) 2Xl +X2 +X3 -X6 = 4Xl - 2X3 +Xs +2X6 = 5

-xj:2:0,j=1,7

trong do, X4, Xs la bien phu, X7 la bien gia, M >° 100 tuy y.

Ta co h~ Anco ban ban dAula {X7,X2,XS}'

0,25

Phuong an co ban ban dAula XO = (0,4,0,0,5,0,2) 0,25

Bang dan hinh:

XB CB PAXl X2 X3 X4 Xs X6

-13/3 -3 2 0 0 -2

x7 M 2 1 0 [3] -1 0 -30,25

x2 -3 4 2 1 1 0 0 -1

Xs 0 5 1 0 -2 0 1 2

f 2M-12 M -14/3 0 3M - 5* -M 0 -3M +5 0,25

Vi M >° 100my y nen ~3 >0·100 nhat, ta chon cQt X3 lam cQtxoay.

Vi tren cQt 3 ta co al3 = 3>° nrong (engvoi ti dan hinh nho nhdt nen ta chon0,25

al3 = 3 lam phan tu xoay.

xB CB PAXl X2 X3 X4 Xs X6

-13/3 -3 2 0 0 -2

X3 2 2/3 1/3 0 1 -1/3 0 -1 0,25

x2 -3 10/3 5/3 1 0 1/3 0 ,0

Xs 0 19/3 5/3 0 0 -2/3 1 0

f -26/3 0 0 0 -5/3 0 00,25

TOAN _MHTKT _CDCQ_A-Q TRANG 2/4-MD: 060514676

Vi f ---+ min va 'if/:). j :s;° (j =1,7) nen phuong an eo ban dang xet la phirong an

t6i Uti.V~y phuong an t6i Uti cua bai toan dang chuan (PM) la: 0,25

• ( 10 2 19 )' 26xM = 0'3'"3,0'3,0,0 va fmin =-).

Vi thanh phan cua bien gia bang 0 nen bai toan dang ehinh Hie(P') eo phuong

, ;.. 1" (0 1° 2 ° 19 0) 'J. 260,25

an t01Uti a xp' = '3'"3' '3' va min =-).

D de bai , b d;' , h ,;.. 1" (0 10 2) 'J. 26 0,25o 0, at toan an au eo p irong an t01Uti a xM = ,--,- va min =--.333

b Id

Vi /:).1=° rna Xl khong la bien eo ban nen bai toan eon eo phuong an t6i Uti

khac. Xet 15' don hinh, ta eo th~ chon all =~ hoac a21 =% lam phan illchu y~u 0,25

va h~ Aneo ban moi kh6ng trung voi h~ Aneo ban da eo nen ta eo 2 each chon

phan illchu yeu.

Chon phan illchu y~u la all =~ ta eo bang sau:

Xl X2 X3 X4 Xs x,XB CB PA

-13/3 -3 2 0 0 -2

Xl -13/3 2 1 0 3 -1 0 -30,25

X2 -3 0 0 1 -5 2 0 5

Xs 0 3 0 0 -5 1 1 5

f -26/3 0 0 0 -5/3 0 00,25

H - h h;' , ,;., 5 "oac e on p an ttr ehu yeu 1a a21 =3" ta eo bang sau:

Xl X2 X3 X4 Xs X6XB CB PA

-13/3 -3 2 0 0 -2

X3 2 0 0 -115 1 -2/5 0 -1

Xl -13/3 2 1 3/5 0 5 0 0

Xs 0 3 0 -1 0 -1 1 0

f -26/3 0 0 0 -5/3 0 0

Bai toan (PM)eo mot phuong an toi Utikhac la

X~I = (2;0;0;0;3;0;0).0,25

TOAN _MHTKT _CDCQ_A-Q TRANG 3/4.,.MD: 060514676

Tir day suy ra bai toan ban dfiu c6 mot phuong an t6i uu khac la x~ = (2;0;0).3d32da

- Sa do m~ng lucri:

0,25

0,25

0,25

0,25- Danh so thir nr cac dinh dung

- Tinh chi tieu thai gian sorn nhat xuat hien SlJ kien dung 0,25

- Tinh chi tieu thai gian muon nhat xuat bien SlJ kien dung 0,25

- Xac dinh chi s6 k, tren So' d6 mang lucri dung 0,25

0,25- Ve ra rang, sach depIdb

- Duong gang la duong noi cac SlJ kien 1,2,4,7, 8. 0,25

0,25

0,25- Ve dung dtrong gang tren So' do mang lucri

- Thai gian hoan thanh dir an la 28 (dan vi thai gian) 0,25

TRANG 4/4-MD: 060514676TOAN_MHTKT_CDCQ_A-Q

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