Đề thi môn tối ưu hóa( quy hoạch tuyến tính)

TrLlang Df;li hQc Kinh T e TP. HeM HQ va ten:

Khoa Toan - Thong ke SBD:____,

~,'~OJ/;G4~ ,

DE THI MON TOI utr HOA (QUY HO~CH TUYEN TiNH)

Thi1i gian lam bai: 75 phut (Kht')ng sii'd1.lDg tai li~u)

(Chu y: Sinh vien phai nqp h,d d~ kern vc1i bai thi)

B~4

Cftu 1. (ld) Cac phat bieu sau day dUng hay sai ? Gifli thfch ly do t'ili sao?

a) Bfli toan QHIT t6ng quat: min f(x) , n€u co X i= 0 va f(x) bi cMn du6"i tren t~p phuong an x t XEX

thi se luon luon co phuong an Cl,l'C bien t6i uu (phuong an cO' ban t6i un).

b) 0 bang don hinh tOi un, n€u Llv =°

v6"i Xv Ia bi€n tl,r do (hi€n phi cO' sa) thi bai toan QHIT se

luon Iuon c6 PATU khac.

Cftu 2. (3,5d) Giai bai toan quy ho~ch tuytn tinh sau:

f(x) = 2xI + X2 + 4X3 + 2X4 ----)- min

Xl - 2X2 + X3 :$; 6

3Xl - 5X2 + 2X3 - X4 = 25

3Xl 6X2 + 4X3 + X4 :$; 20

Xj ;;:: 0 U=1,2,3,4).

Tim phltdng an t6i l1U kba.e, ne'u co.

cau 3. (3,5d) Xet bai toan v~n tii vdi s6lil$u eho nhlt san:

3 5 8 J (aJ (30, 50, 80);

(cij) = 8 5 6;

[ (h) = (30, 70, 100). 6 10 10

a) Giai bai toan v~n tii tren.

b) GiM bai toan v~n tii tren vdi dieu kil$n diem thn thll 3 nMn dii hang.

cau 4. (2d) Cho bai toan QHTT sau:

f(x) = - 3Xl + 3X2 + X3 + 2X4 ---+ min

- 2xI + X2 + X3 + X4;;:: 2

- 2Xl + 2X2 + X4 10

XI - X3 :$; 5

Xj;;::

°

(j= 1,2,3,4).

a) Vi€t hai toan dOi ngau.

b) Bi~t bai toan tren co phuong an tOi un Ia.: x· = (3, 8,0, 0). Hay dung Binb ly dq l~cb bit yiu

d€ tim tAt ea cac phuong an Wi uu cua hai toan dOi ngau.

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