Đề thi môn Tối ưu hóa ( Quy Hoạch Tuyến Tính)

HQ

TrLlCJng fJ?i hQc Kinh Te TP. HeM
Khoa Toan - ThtJng

va

ke

SSD:

"~JIOJ J. (b~

DE THI MON TOI

uu HOA (QUY HO~CH TUYEN TiNH)

sa

ThO'i gian lam bai: 75 phut (Khong
d"ng tai li~u)

(Chu y: Sinh vi~n phai nQP la)i d~ kern v8i bai thi)

D~2


cau 1. (ld)

Cac phat bi~u sau day dung hay sai ? Gicii thich 19 do t~i sao?
a) Bai toan QHTI: max f(x), chi co 3 PACB la Xl, X2, X3 thi gia trj t6i

U'U

hI:

xeX

max {f(x 1 ), f(x 2 ), f(x 3 )}.
b) Blii toan QHTI (P), them bi~n gici thanh bai toan rna rQng (PM), n€u (PM) co PATH thi (P) se
luon luon co PATH.

cau 2. (3,?d) Giili bai toan quy ho~ch tuy€n
f

Hnh sau day.

6x( + 4X2 + 3X3 ----)- max
2xJ + X2 + X3 :5 24
2xI + 2X2 + X3 = 18
XI + X2 + X3 ?: 18
X), X2, X3 2: O.

Tim phuong an t6i

U'U

khac, n€u co.

cau 3. (2d) Cho bai tot'm quy ho~ch tuy~n tfnh sau day:
4Xl + 6X2 + 2X3 ----)- min

2Xl + X2 + X3 :5 24
18
2x( + 2X2 + X3
Xl + X2 + X3 > 18
XI. X2, X3 2: O.
a) Vi€t hai toan d6i ng~u.
b) Biet bai toan tren co phuong an t6i U'U hI: x· (0,0, 18). Hay dung Diob It d9 I~cb bil ySu d~
tim tftt cil cac phuong an t6i U'U cua bai toan d6i ng~u.

cau 4. (3,5d)

Cho bai toan v~n tili vo; s6 li~u sau day:

1 63 4]7;
[6 4 8

(c jj ) = 3

(aJ=(10, 50, 90);
(b) = (10, 40, 70).

a) Gi:ii bili loan v~n tM tren.

b) Giiii bai toan v~n tai tren vdi di~u ld~n di~m ph:it thti' 3 pMt he't hang.