Đề thi môn tối ưu hóa( quy hoạch tuyến tính)
Trang 1TrLlang Df;li hQc Kinh T e TP HeM HQ
Khoa Toan - Thong ke
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DE THI MON TOI utr HOA (QUY HO~CH
Thi1i gian lam bai: 75 phut (Kht')ng sii'd1.lDg tai (Chu y: Sinh vien phai nqp h,d d~ kern vc1i
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
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 :$;
3Xl - 5X2 + 2X3 - X4 =
3Xl 6X2 + 4X3 + X4 :$;
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$u eho nhlt san:
3 5 8 J
(cij) = 8 5 [ (h) = (30, 70, 100)
6 10 10
a) Giai bai toan v~n tii tren
b) GiM bai toan v~n tii tren vdi dieu kil$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
d€ tim tAt ea cac phuong an Wi uu cua hai toan dOi ngau
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