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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:- T! E+ O7 \9 @! z
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:
' R% e$ O7 {! c1 `3 dmax 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x339 H6 n- T$ \! W/ r
st: v* Q3 c( s4 ~2 \# m
x34=0;8 L2 N. s, A4 m, R1 I1 g0 c `
x11+x12+x13+x14<=50;* c+ j1 G" }# W6 g$ K, j% S) [ h
x21+x22+x23+x24<=60;6 w: `4 o$ F, S8 e+ B
x31+x32+x33+x34<=50;
h6 U! @& g) L! `x11+x21+x31>=30;
6 {% E! V& A0 n* b9 F* ex11+x21+x31<=80;
. K: } N1 `% F1 g% X" R* g" N8 ~x12+x22+x32>=70;- d" g. m0 L) A ?8 s
x12+x22+x32<=140;) z4 ~! _6 Y) r) }
x13+x23+x33>=10;! f3 K' |% o, z9 K: N( t
x13+x23+x33<=30;! Z7 J+ W% M/ G- t5 y
x14+x24+x34>=10;& M, ?0 B& Y4 c. c O
x14+x24+x34<=50;3 ~5 V6 X- }/ r9 j( V7 t& t- H
end& t" |4 j3 h1 v5 O+ h) `- u; U2 l
LINGO程序:: E5 y6 l, o! p" K9 s: B$ q
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
) d2 m8 f# o7 n0 X" Yx11+x12+x13+x14<=50;
& ^& d; g9 ~3 j* P% |x21+x22+x23+x24<=60;9 B$ d1 P8 r+ |6 F+ g7 K
x31+x32+x33+x34<=50; x2 `* |& Z. A M
x11+x21+x31>=30;# q+ X6 g( c, l7 i' _ T" M; [
x11+x21+x31<=80;
1 r; ~" u4 K# F9 q/ J cx12+x22+x32>=70;5 N) N4 n7 b% X4 u0 |' `0 Y/ R" H
x12+x22+x32<=140;
; v6 g( }' T1 ]# R4 V& N* m- X# Sx13+x23+x33>=10;. M1 `6 C: m: j# E: q& D+ U% e, ~
x13+x23+x33<=30;
% Z+ u/ Y8 w3 ~+ v" i @ R& Dx14+x24+x34>=10;
% E/ O2 r: k. M0 L1 D& Xx14+x24+x34<=50;. [; c- ^* ]% \+ t8 p' P) K
end+ N. W0 L5 A j/ `
运行结果:
. L& Y4 V) Z* t8 D7 p; T i: V* Z Global optimal solution found.# }# X6 G8 w+ P8 [
Objective value: 47600.006 i0 H) z* ` z% p2 [" D- `
Total solver iterations: 73 V( _$ V% O9 c, I) A! B# I
$ U+ K/ x! l: ]8 {! k, h6 b5 g! m) T, V
Variable Value Reduced Cost
7 w; n% c! R/ y% r' cX11 0.000000 30.00000
# R& P% ~9 |) k$ V; U/ PX12 50.00000 0.000000
1 G7 u( O8 t$ iX13 0.000000 50.000004 C: T* l; { }! E+ i
X14 0.000000 20.00000
2 H- B7 d$ x: V% e' f9 oX21 0.000000 10.00000
4 h5 C& @1 p3 s: y. TX22 50.00000 0.0000008 v; ?# x! K/ ~" E u
X23 0.000000 20.00000' D4 {0 h# h# u$ G; T' u6 d
X24 10.00000 0.000000
, {# e$ ^/ T1 Y/ ^X31 40.00000 0.000000; B0 \8 M/ V3 J/ q! X
X32 0.000000 10.000000 |2 m8 I7 g# `$ x& N
X33 10.00000 0.000000
1 E1 T) D( A4 Q+ n2 s/ @# E% c& i/ C+ pX34 0.000000 240.0000
, A+ W4 _/ }' R
: S3 J; I# z; U/ y. d$ _Row Slack or Surplus Dual Price
7 t: Y5 d* A: Y' {. d1 47600.00 1.000000% J7 X2 `# k; j% y6 {! I6 }
2 0.000000 320.00008 w7 u. p# `: Z0 s+ I e& ^
3 0.000000 320.0000$ h$ ~& A1 I5 G2 m
4 0.000000 260.0000$ s- a0 r- _1 u7 t# U+ Z. W: ~
5 10.00000 0.000000
1 Y. k6 \" ^6 ~6 t6 40.00000 0.000000
( v9 L- Y M) M/ K% s9 _7 30.00000 0.0000006 ` A# R4 i# l& u" i0 r4 T
8 40.00000 0.000000
9 p9 W$ i* V0 f6 \' E' L9 0.000000 -40.00000
7 C8 B7 Y- Z9 v6 W) ^10 20.00000 0.000000
" P9 ~$ {6 Y5 i O" R11 0.000000 -20.00000$ A' R M' ?7 Y2 r
12 40.00000 0.000000( F) y* R9 A4 J) l) g$ z
7 a- }: o0 `2 \/ t( m2 a G
【2】求解:
9 U+ e% n6 Y9 v" C/ a模型:+ p, _& f0 n! Q. p ^
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
N" X/ ]+ O. t5 zst! m0 W+ U T5 o, M$ b
x34=0;
8 H( H6 p" T% R. Vx11+x12+x13+x14<=100;" I: ?% y- V4 ~9 V& F" x9 r3 W
x21+x22+x23+x24<=120;
9 j( n9 t1 v( C# } Rx31+x32+x33+x34<=100;
, A- {# \: `3 kx11+x21+x31>=30;
1 |4 e# H( H; `x11+x21+x31<=80;
) P" R8 X+ a. T) b' z( i: J* ox12+x22+x32>=70;
9 @' y! |" y8 a3 d# W3 nx12+x22+x32<=140;- @+ j4 |# X; t; ^" O
x13+x23+x33>=10;
! l# i7 ?8 f9 S6 T$ w1 v" vx13+x23+x33<=30;: M0 J2 \2 a7 D& S0 U5 ~
x14+x24+x34>=10;
6 b1 g3 J" ^: W7 X* Yx14+x24+x34<=50;
1 K( q2 h. U$ j) x& tend5 w2 G, P* p' ]$ i+ | T
LINGO程序:2 |( K: `& R/ B# C5 `/ Q" u, M
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
5 k* J) `! h* E) i# ]0 [7 ax11+x12+x13+x14<=100;' }6 k1 d- g+ `) _
x21+x22+x23+x24<=120;
- }& {" S3 R3 t, B( e; |' Ex31+x32+x33+x34<=100;3 L: J1 H) e2 T* n3 x1 z! H
x11+x21+x31>=30;
/ Z2 `4 f8 w/ n; Cx11+x21+x31<=80;
. q% R4 G/ g n/ `. \ f0 _1 ox12+x22+x32>=70;
8 @5 p0 E- h6 s7 l6 i! f! sx12+x22+x32<=140;+ ~: X; n0 W9 B" t* M8 R
x13+x23+x33>=10;
1 |, y$ K: W; T: Y1 ^/ A% Cx13+x23+x33<=30;5 G4 `9 O3 g0 h- _8 g2 H, u
x14+x24+x34>=10;
" K/ T, F; J7 [1 a% Sx14+x24+x34<=50;
$ {% @" ]% C. d0 W9 Zend$ R- j g# o0 ]( g# I8 i! X
运行结果:
: b6 I5 a4 B) c! X, ~ Q Global optimal solution found.
# _, v& S6 D/ n) D! J- ^ Objective value: 88700.00
& z% v9 b( L9 y* M% d' y: r Total solver iterations: 78 N& H7 s; [7 j+ N0 u! x! A
1 M3 ]0 j2 ~% b5 K* Z
# {1 p+ Q9 _7 N) d- }: v! v( H
Variable Value Reduced Cost1 k0 s2 o9 L. }+ W
X11 0.000000 20.00000
. ]0 K! G5 F# IX12 100.0000 0.000000* l8 j M6 E: v) q4 t+ N' |
X13 0.000000 40.00000
; w& L T% m% B. N; PX14 0.000000 20.00000
. O. f" k; Q _) y: f: T, l$ c K" o# xX21 30.00000 0.0000001 b0 e$ d4 _" p* w: ]8 z6 X
X22 40.00000 0.000000
% H; b4 o, u/ T) X$ FX23 0.000000 10.00000$ ]* _% c4 @- Q: f8 @
X24 50.00000 0.000000
6 q) V+ i& _& H- N9 [$ W: {4 SX31 50.00000 0.0000000 w! A0 j' I% ^' K6 O3 k: Q
X32 0.000000 20.00000" e7 h6 j" p) a; o, j
X33 30.00000 0.000000+ ^: W! O \8 j. ]
X34 0.000000 250.0000+ o- H- p! U0 u6 N: R5 V; D% n/ _4 O
* p) M$ [) `: P u' eRow Slack or Surplus Dual Price4 {. O6 G$ t# J/ H
1 88700.00 1.000000
3 I$ R: ]5 H9 D! }1 q2 G2 0.000000 50.00000; r( g6 k. f8 G# ?0 R$ W
3 0.000000 50.000001 J8 W+ R# P! D0 r4 a' ~# _' J
4 20.00000 0.000000
' q$ `- \8 s( E5 50.00000 0.000000+ O" Y J4 |& J$ H8 q1 t$ C
6 0.000000 260.0000
8 A" u/ e' T6 a7 70.00000 0.000000
4 T+ D+ F4 Y+ H% W' k" k y8 0.000000 270.0000; r1 {" R4 v& ~" t2 y3 L* w
9 20.00000 0.000000
0 o, `1 x$ b* h9 {- F" ^10 0.000000 220.0000; p1 v3 b' [! @! B3 R* t
11 40.00000 0.000000$ a2 l0 {6 V: c/ s& F
12 0.000000 250.0000 |
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