Nguyễn Ngọc Phan Văn

1. flAp AN flE THI HQC PHAN: MD HINH ToAN KINH TE
M§ hoc phin: TOKT022 sA tin chi: 02
Khoa: _ Caoding h~Chinh quy
Ngaythi: / / Sirdung tai lieu: Duoc D Khong dUQ'cG]
Cau y NQidung fli~m
1
2d
Mo hinh toan kinh te gom cacbien sova cach~thirc toan h9Clien h~ gitra cac 0,25
bi€n s6.
Cacbien so cuamo hinh g6m:
- Bi€n nOisinh 0,25
- Bi€n ngoai sinh
- Tham s6
Moi lien h~ giira cacbien so: diroc the hien bang cacbien thirc, h~thirc toan 0,25
h9Crnaph6 bien nhftt la cacphuong trinh g6m cac loai
- Phuong trinh dinh nghia
- Phuong trinh hanh vi 0,25
- Phuong trinh di~u kien
Cho vi du ve mo hinh toan kinh te dung 0,25
Ghi chu ra rang 0,25
Giai thich dung cacbien 0,25
Giai thich dung cacmoi lien h~ 0,25
2
5d
a
3d
* Dira bai toan ve dang chinh tac:
_Vi rang buoc 2 co v€ trai IOnhon hoacbangvSphai nen ta b61:v€ trai cua
rang buoc 2 mot bi€n khong am Xs'
_Vi rang buOc3 co v€ trai be hon ho~cb~ngv€ phai nen ta them v€ trai cua
0,25
rang buOc3 mOtbi€n khong am X6·
_Vi rang buOcbi€n co Xz ~ 0 nenta thay Xz boi -Xz trong toan bObai toano
_Vi rang buOcbi€n co X3~ 0 nenta thay X3 boi -X3 trong toan bObai toano
D~ng chinh tac cuabai toan dacho la
f = Xl +4X2 -3X3 -3x4 ~ max
(P')
r-"+5x,- X, +3x,~ 1 _ 0,25
Xl -4X2 +2X3 -3x4 -xs --3
-xl-2xz -X3 -2X4 +X6 =4
-
Xj~0,j=1,6
TOAN_MHTKT_CDCQ_A-Q TRANG 1I4-MD: 060514675

2. * Dtra bai toan ve dang chuan:
_Vi rang buoc 2 co v~ phai am nenta nhan ca hai v~ cho -1. 0,25
_Vi rang buoc 1 chua co bi~n co ban nenta them vao mQtbi~n gia X7·
Dang chuancuabai toan da cho III
f = Xl +4X2 -3X3 -3X4 +Mx7 ~ max
(PM)
rXI+Sx, -x, +3x4 +X, ~~
-Xl +4X2 -2X3 +3x4 +X5-3 0,25
-Xl -2X2 -X3 -2X4 +X6 =4
-
Xj ;;::0,j=I,7
trong do, X5' X6 hi bien phi), X7 la bi~n gia, M < °be my y.
Ta co h~ Anco ban ban dAuIII {X7,X5,X6}
Phuong an co ban ban dAula XO = (0,0,0,0,3,4,1)
0,25
Bang dan hinh:
XB CB PA
Xl X2 X3 X4 X5 X6
1 4 -3 -3 0 0
x7 M 1 2 [5] -1 3 0 0
0,25
X5 0 3 -1 4 -2 3 1 0
X6 0 4 -1 -2 -1 -2 0 1
f M 2M - 1 5M- 4* -M+ 3 3M+3 0 0
Vi M < °be tuy y nen ~2 < °be nh~t,ta chon cQt X2 lam cot xoay.
Vi tY dan hinh ')..= min{~, !}= ~ nenta chon al2 = 5 lam phan illxoay.
0,25
Bang dan hinh moi: .
XB CB PA
Xl X2 X3 X4 X5 X6
1 4 -3 -3 0 0
x2 4 1/5 2/5 1 -1/5 3/5 0 0
1115 -13/5 -6/5 3/5 1
0,25
Xs 0 0 0
X6 0 22/5 -1/5 0 -7/5 -4/5 0 1
f 4/5 3/5 0 11/5 27/5 0 0 0,25
Vi f ~ max va V~ j ~ °(j = 1,7) nenphuong an co ban dangxet III phuong an
0,25
t6i uu.
V~y phuong antoi uu cuabai toan dang chuan(PM) la:
• (1 11 22 )' 4
0,25
XM = 0'5,0'0'5'5,0 va fmax=5·
TOAN_MHTKT_CDCQ_A-Q TRANG 2/4-MD: 060514675

3. 3
h ,;.. 1" (0 1 0 0) 'I' 4P irong ant01iru a x(P) = '-5" va Jrnax = 5 .
3d
Vi thanh phan cuabien gia bang °nenbai toan dang chinh tac (P') co phuong
, ;.. 1" (0 1 0011 22) 'I' 4 D d' bait ' b d;" ,ant01tru a x(P') = 's" 'S'5 va Jrnax =5· 0 0, ar oan an auco 0,25
b
2d
0,25
2Yl +Y2- Y3;?:1
-5Yl +4Y2 +2Y3 ~-4
0,25
Yl -2Y2 +Y3~3
3Yl -3Y2 -2Y3 ;?:-3
0,25
Yl tuy y, Y2~0'Y3 zO 0,25
G9i y* = (Y; ,y;,y;) laphirongant6i iru cuabaitoand6i ngdu (D).
* Sir dung h~ thirc: x;(taijY;-cj ) = 0, j =1,4 ta diroc phuong trlnh 0,25
(1)
* Su dung h~ thirc: Y; (±aijx~-bi) = 0, i = 1,3 ta ducc Y; = Y; = 0
J=l
0,25
h •• '() d • 4T ay Y2'Y3 vao 1 ta UQ'C Yl =5· 0,25
~ , s , ".,;'.?::" (4 )' 4Vay, phirong ant01iru cuabai toan dOl ngau 1a:Y = 5;0;0 va frnin = 5. 0,25
Sado mang lucri:
TRANG 3/4-MD: 060514675TOAN_MHTKT_CDCQ_A-Q

4. - Ve dung cac cong viec Yl'Y2'Y3'Y4 0,25
- Ve dung cac cong viec Y5'Y6'Y7,Yg 0,25
- Ve dung cac cong viec Y9'YJO'Yl1'Y12 0,25
- Ve SO' do ro rang, can doi 0,25
- Danh sotlnr tu cac dinh dung 0,25
- Tinh chi tieu thai gian s6m nhat xuat hien S1' kien dung 0,25
- Tinh chi tieu thai gian muon nhat xuat hien S1' kien dung 0,25
- Ghi chi sf, k, tren sa db mang lucri dung 0,25
- Ve dung dirong gangtren sa do mang lucri 0,25
- Duong gang la duong noi cacS1' kien 1,2,4,6, 7, 8. 0,25
- Cac cong viec tren dirong gang: Yl'Y4,Yg'Y9'YlI 0,25
- Thai gian hoan thanh dir an la 31 (dan vi thai gian) 0,25
TOAN_MHTKT_CDCQ_A-Q TRANG 4/4-MD: 060514675