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群组: 数学趣味、游戏、IQ等 群组: 数学建模 群组: 趣味数学 群组: Mathematica研究小组 群组: 我们的小窝 |
【1】求解:4 y% e) Y3 B9 \
设水库A、B、C分别向甲、乙、丙、丁四个小区供水量为x11、x12、x13、x14、x21、x22、x23、x24、x31、x32、x33、x34,则有:% n+ o- ^+ ~1 X- B
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x339 B; ?" G. c6 c. K0 S [
st
# G) s8 g/ C0 ?5 U0 I/ L9 lx34=0;( K6 M7 b ~& \8 |" P1 D3 _
x11+x12+x13+x14<=50;
; v0 o+ i/ {: P/ r. M6 W) nx21+x22+x23+x24<=60;
$ A% E7 Q# R+ L& hx31+x32+x33+x34<=50;( r; |' A; V1 I8 j' H1 M
x11+x21+x31>=30;
* m: E. N5 v8 f& ]x11+x21+x31<=80;5 L3 k% u; T' B$ J) F5 W. G
x12+x22+x32>=70;
" }( k d8 H8 Y W9 Rx12+x22+x32<=140;6 i! m- s! z- z! \: ]9 e4 E9 H
x13+x23+x33>=10;7 e4 {9 b' |$ v' q3 v t
x13+x23+x33<=30;8 }. R4 e' d# ?9 t
x14+x24+x34>=10;
4 r5 i$ P$ d& p: ^- f4 lx14+x24+x34<=50;
: z% K9 D3 B' F! h! R+ Mend+ J" ^ w2 H0 u: Z
LINGO程序:
+ w V- R, A4 u- nmax=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
. R* B/ V3 b1 i5 ]; [- o0 L" P* ix11+x12+x13+x14<=50;
n$ U) d# J9 E' Nx21+x22+x23+x24<=60;
. a; B1 X% e& m4 Fx31+x32+x33+x34<=50;
! m2 t# H' C/ }+ W/ r$ ?) @; [+ ~% ix11+x21+x31>=30;3 {) Y d2 a3 B$ x9 t
x11+x21+x31<=80;" i' t# w; S9 y; Q0 L
x12+x22+x32>=70;
& N+ R* z. e* Y) y: Xx12+x22+x32<=140;- z1 d ]7 N- k( a
x13+x23+x33>=10;0 I7 a+ M, t# Z$ d
x13+x23+x33<=30;7 t2 [( [1 R- [3 k' B' T5 k5 g
x14+x24+x34>=10;/ ^7 b) B4 j# d8 A3 U* t; C
x14+x24+x34<=50;
: H5 v3 k1 _. }+ p& Y" b2 Vend
2 ^' z, X# K! l1 v3 O% C4 u8 D运行结果:
9 X) o1 N8 U$ ]# O Global optimal solution found.
4 N5 q% f* e; J0 c Objective value: 47600.000 n! K6 f# P! {3 p1 S
Total solver iterations: 7
$ w9 y6 v- j% Q7 K e+ V( @$ |, ` ~# F9 m
2 N5 } M* p; q; F; [ W
Variable Value Reduced Cost: u2 O2 y2 C/ U7 m# z/ X
X11 0.000000 30.00000
# t; U$ v- ]4 g ZX12 50.00000 0.000000" ?+ U/ ^; u* O+ e7 K$ u4 [ Z
X13 0.000000 50.00000
! S {3 ^9 V, |3 f* oX14 0.000000 20.000008 e/ j8 J" g7 ^$ ^' I9 c% k5 D0 ?, C
X21 0.000000 10.00000
G# Q+ ? X2 A- D2 o' b+ @- hX22 50.00000 0.0000009 ]2 N4 c4 M% b% p' ?
X23 0.000000 20.000004 S# t- V$ x6 x# y
X24 10.00000 0.000000, {4 e4 b" }4 u
X31 40.00000 0.000000
$ J9 B: n( q+ H- ZX32 0.000000 10.00000
' m, Z j: b2 ?/ m/ ]5 l/ AX33 10.00000 0.000000$ E( ]( g* i+ ]2 d& e: w
X34 0.000000 240.0000
; r6 o: Q& C( {, s+ I3 Q; G2 b, V4 L" M/ Q! |, n
Row Slack or Surplus Dual Price" i! J# y: \, G( S q4 M: A
1 47600.00 1.000000. c, c4 e3 O& R
2 0.000000 320.0000
6 y( l0 H O9 D3 0.000000 320.00002 v: x; Q# }) }+ A
4 0.000000 260.0000
0 U" ^& ^5 l) W; E, q8 Z5 10.00000 0.000000
7 w- Y: j: K2 ?1 T, Y* W6 40.00000 0.0000008 r3 } [, ^* b
7 30.00000 0.000000' `+ ?$ l9 o- o
8 40.00000 0.000000
3 } ~" D% b" b9 0.000000 -40.000008 b e# R; x4 ]! Z* n0 n* F6 C5 j
10 20.00000 0.000000
! p: t& J! M7 a- [7 u. H: W% L1 E11 0.000000 -20.00000
. g! t, S1 x5 r7 C S( p; b12 40.00000 0.000000
L2 l" p" T# w# }! d' x
" C3 @- E& [7 U5 f. T, v' L【2】求解:
* i* F! |' e- L2 {9 y( M2 f模型: r! H9 B* m- J6 c {
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33- C! b/ S) f- A _0 `
st7 {/ w5 ?$ l* f( p4 y$ i
x34=0;
G N. B, R. |5 Q, ^' g' S, px11+x12+x13+x14<=100;
: [, L; l4 |; sx21+x22+x23+x24<=120;
0 z {# ?4 y3 h3 L2 Cx31+x32+x33+x34<=100;7 R% |1 A- Y4 T7 G' ]2 A) K
x11+x21+x31>=30;2 _0 D& ?# ~1 o' V/ r. i& T
x11+x21+x31<=80;* o+ I5 x/ h- t( X5 k% Q
x12+x22+x32>=70;6 y5 D3 s9 P+ Z; p$ {, {7 [0 d
x12+x22+x32<=140;
# I2 J5 A1 H7 |/ Q7 \, N7 kx13+x23+x33>=10;
/ W T) x5 p- i, K" f- o- Bx13+x23+x33<=30;
9 ^: p5 C0 H! y& ~7 I5 o" P jx14+x24+x34>=10;. [, ]: \4 w& z* |/ e
x14+x24+x34<=50;
, _8 L4 V* m" Vend1 U% @* ?) U% B, y4 S
LINGO程序:7 i8 x) `% f. p2 @4 o- e& l( y4 W
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
& |* g: X$ Y- g. H3 i. v" P: J& ex11+x12+x13+x14<=100;
9 {* |7 I1 P; f' ]& ox21+x22+x23+x24<=120;
# k7 I( r. e$ u, kx31+x32+x33+x34<=100;4 M- m& {: N7 U% g
x11+x21+x31>=30;
+ ?% e: q5 J2 C* y; R$ px11+x21+x31<=80;
- s9 f* P! u+ I, c+ }x12+x22+x32>=70;
) r( W+ J+ P# |0 V) @6 px12+x22+x32<=140;
" k: O. y& r) ^x13+x23+x33>=10;- M+ T! q/ W9 s! s+ Z' @" |
x13+x23+x33<=30;; P# A, ~/ i& |
x14+x24+x34>=10;
: w- {& k/ [/ ]& ~& t& P- c+ w5 I5 |x14+x24+x34<=50;
- M6 w S3 e% a' F; C& qend# ]. C4 ` J8 {) g- U. s
运行结果:
. @6 f4 g. {. ]. o$ |, r' L- c Global optimal solution found.
" D7 s# W: b% n! z% z, I5 E& u Objective value: 88700.00 O; M. J5 o) e( z( @" R2 |7 N
Total solver iterations: 7
! i! t- A* x$ y2 C
+ I6 N) s" n( W# c
9 ]$ Q0 g+ A* g; D9 ^Variable Value Reduced Cost
: }8 A' S3 k# C+ FX11 0.000000 20.00000
) S V0 c$ x% U% ?6 n- R; sX12 100.0000 0.000000$ M4 S* f4 m! C) J2 e' D" H& F6 c
X13 0.000000 40.00000& Q* D0 u% G; r! L2 h+ o. S
X14 0.000000 20.00000
* q |3 c, W% e( x* pX21 30.00000 0.000000( {$ ?, k4 o W& q
X22 40.00000 0.000000' v( Z. j( E0 |+ b4 b
X23 0.000000 10.00000
* [" a, Z4 `% eX24 50.00000 0.000000( Q. J: U1 O( |2 h0 w; P& F5 e
X31 50.00000 0.0000005 t% e9 p, |; c- F% {9 w; i9 l
X32 0.000000 20.00000, w O D3 p4 S1 X- o5 L
X33 30.00000 0.000000! N/ f2 ]0 I& a& r: R
X34 0.000000 250.0000
6 w4 X6 j# [/ d/ `- Q& P
; x$ X3 i, ?6 E0 a) yRow Slack or Surplus Dual Price( h: X* @* U( S' I' L
1 88700.00 1.000000# _# F1 h3 |% E
2 0.000000 50.00000
- s/ g8 _/ s4 v, V; @& T8 Q+ s, J3 [3 0.000000 50.000009 w9 Y# R/ i; m( }! A3 b
4 20.00000 0.000000
- _, Y5 R+ i3 l/ w' h ~5 50.00000 0.000000
' O2 E+ Y b: C7 U# v6 0.000000 260.0000
# A! B; ?& h9 G' I: ?; j' E, Q7 70.00000 0.000000
# y% l1 y; Z: w% J" f1 ]8 0.000000 270.00002 s$ l2 f6 e; d; f) v' T
9 20.00000 0.000000
. J7 T/ p& X: D- @10 0.000000 220.0000
7 r L1 L6 ?- v% s( L11 40.00000 0.0000009 q" R4 B$ M2 p5 d+ w
12 0.000000 250.0000 |
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