Đề thi môn Tối Ưu Hóa( Quy Hoạch Tuyến Tính )

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HQ va ten:


Trliong D.;li hQc Kinh T TP. HeM
Khoa Toan - Thtfng ke


\<.~WA -. (l(Q

DE THI MON TOI lfU HOA (QUY HO";'CH TUYEN TiNH)

Thili gian lam bai: 75 phut (Khang sil d\lng tai li~u)

(Chu y: Sinh vi~n phai nqp ll(li d@ kern veti bai thi)


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Olu 1. (2d) MQt nba. hang-kMch s:,ln c6 4 phong hQi nghj A, B, C, D. (j m6i phong c6 mQt s6 vj tri

c6 the lAp d~t camera quan sat (xem sa de). Camera liip (j vi
tri 1 thl chI quan sat dUQc phong A, camera lAp (j vi tri 2 thl

\
(1) . A
\

j

~

quan sat dUQC phong A va phong B, tlfong til cho cac camera
con l:,li. Phong D la phong VIP nen dn It nhdt 2 camera de

0·

quan sat, cac phong con l~i chi dn it nha't 1 camera de quan

'4

sat. M6i camera c6 chi phi la:p d~t la 500USD, t6ng s6 ti~n

\..;

Hip d~t cac camera khong vu<;1t qua 2500USD.
Hay xac dinh vi td Hlp d~t cac camera sao cho: t6ng s6

C

camera liip d4t la it nhdt, nhtrng v§.n bao dam di~u ki¢n v~
an ninh va dieu ki¢n v~ t6ng s6 ti~n dau tu1 Yeu du chi l~p
mo hlnh, khong giaL

Cau 2. (3d) Giili bai toan quy hO{lch tuyen Hnh sau. Phucmg an t6i uu tim dU<;1C c6 duy nha't? T:,li sao?
f=2xl
XI
2xI
2x I

+X2 +x3~min
- X2 - X3 :::; 2
- X2 + X3 :::: 2
+ X2 + 2X3 :::; 8
X., X2, X3 ?; O.

ca u 3. (2d) Cho bili toan quy hO{lch tuyen Hnh sau c6 phuong an t6i uu Iii x·

=

(0, 13, 1):

17xl + 10x2 +4X3~ max
3xJ + X2 + 7X3 :::; 20
Xl + 5X2 + X3 :::: 0
4Xl + 3X2 + X3 = 40
XI:::; 0, X2 tuy 9, X3 ;:: 0.
Hay vie't bai toan d6i ngAu va tim phuong an t6i l.fU clla bai toan d6i ngAu.

cau 4. (3d) Giai bai toan v{in tai v6'i s6 li~u sau day. Tim phuong an t6i uu khac, neu c6.

(c i)

10 8 12J
15 10 14;
[
9 11 12

(a) = (100, 150, 80);
(b) = (120, 130, 50).