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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: _" C6 u0 m9 s* w( v8 O( 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:+ _" s8 f+ k5 ?& t( l9 K0 r
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
8 H0 Z6 X, ]( t& s$ a2 bst
0 P, c/ H& Q8 r% \' Mx34=0;
8 u1 q" N# f V1 a( ^; X. D7 Dx11+x12+x13+x14<=50;, g9 R1 v; _0 V% Z& ^1 |/ f, K9 q
x21+x22+x23+x24<=60;
2 ]! R2 F9 Y j$ f. ]3 b2 Qx31+x32+x33+x34<=50;
0 U( T" O2 C: Cx11+x21+x31>=30;! @6 b0 R) M; w" E
x11+x21+x31<=80;
% a: ]& W- R6 y7 yx12+x22+x32>=70;8 k, U* N/ B1 e7 A2 U$ ]5 A' o7 C, E
x12+x22+x32<=140;" a4 T* L! t! x3 c1 P4 d/ O0 w
x13+x23+x33>=10;
2 k1 ~& C \( ?. O# jx13+x23+x33<=30;4 ^& e o/ J% {8 ^
x14+x24+x34>=10;7 _- ?1 w4 B9 Z4 y9 K: r
x14+x24+x34<=50;8 K$ n4 C: @& j8 @1 u
end
$ m+ [8 }6 M& `9 _) Z/ jLINGO程序:- g) M, U9 _' @" p' [
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;$ y9 A4 ^7 Z+ x2 l8 _
x11+x12+x13+x14<=50;- h& e4 }( V5 d( _# a( u
x21+x22+x23+x24<=60;7 M0 q' r& t! @3 P" ~# w) i
x31+x32+x33+x34<=50;
/ X5 Y/ t4 }0 U) Z, Q wx11+x21+x31>=30;0 r% d4 N& I" _* s
x11+x21+x31<=80;
`9 @* r6 @! l% P7 q1 Hx12+x22+x32>=70;: f( h( C" F h8 h
x12+x22+x32<=140;
. l) N# D* c0 M5 M) r6 Nx13+x23+x33>=10;
4 q( C" s" W! L& O1 lx13+x23+x33<=30;$ r, a4 t9 e; c/ L! k1 @
x14+x24+x34>=10;
$ R4 }- V# m7 `& ~. {+ \" W8 G1 xx14+x24+x34<=50;, D2 C& C, l, s6 m" I
end/ z, }/ G; j6 S( w& s& \8 m
运行结果:) D8 u! M, K+ m& ]
Global optimal solution found.+ w, j( y% h! z$ Y- _ t
Objective value: 47600.00/ P# i5 s6 f/ O; E* z' Z$ T! T
Total solver iterations: 7
/ Y+ ]: V& v" j9 Q' F& P' Y8 l# D" k6 g4 j+ N: r. m( l2 \& y/ A
) Z" x! n, J3 l, G8 C a8 @
Variable Value Reduced Cost- c% I9 A4 ? q: f% s
X11 0.000000 30.00000
- v! k) }. Z, j; f. T8 I/ hX12 50.00000 0.0000004 R# e+ m r" Z7 `. r
X13 0.000000 50.000004 t6 S* k# W, e9 n
X14 0.000000 20.00000
# ?+ E3 j" e$ p! p3 KX21 0.000000 10.00000 Y% J: I. i! X, z* F' u y2 X
X22 50.00000 0.000000
- q3 ~! r8 F8 S) [- F) Q7 u; Z6 P0 XX23 0.000000 20.00000; `$ x n" ]0 E& r$ \) H
X24 10.00000 0.000000% _6 y3 a' `' C6 z: }- z, _
X31 40.00000 0.000000
$ l; h, I6 u3 L3 [X32 0.000000 10.00000
% m& ?0 M7 j, h+ E& c5 J! S7 WX33 10.00000 0.000000
" @& u/ H5 `9 j# l) c/ LX34 0.000000 240.0000. I* F) D1 U: l* R! C0 a# V7 {
; J8 T( I1 ] `9 Y' T. K8 XRow Slack or Surplus Dual Price
: M2 y1 Q2 h6 v5 W8 w: H; x1 47600.00 1.0000002 L4 a n: b6 F) S" k8 x
2 0.000000 320.0000
_% j4 s4 B) Q0 _3 0.000000 320.00005 C f' ~/ [5 q; o9 f' g
4 0.000000 260.0000$ g( k8 @5 e' x5 C) i
5 10.00000 0.000000$ U& o: M# [0 c
6 40.00000 0.000000
/ v) d% t& q e3 @- e7 30.00000 0.000000/ @8 ~0 w8 |/ X% ~9 r a
8 40.00000 0.000000
, T1 v. U; R6 w! \6 X9 0.000000 -40.00000 i- _7 ^9 ^- R) W- b. C: }. n
10 20.00000 0.0000001 v, W" R$ V; W$ R) O
11 0.000000 -20.00000& l" \$ Q. f' O# {7 n& e
12 40.00000 0.000000
}5 d+ l* ~' D5 x s& N, u
3 y; f( q' a" ?2 S; b& @【2】求解:
1 Z0 G* ?: L8 C模型:6 d, p" d7 ]( R" w5 B
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
d7 e) Z* _% Y) ]0 J; k1 G5 Wst7 k! J8 R/ A; D4 q& p
x34=0;! U; Y/ q2 J$ _$ J% m! D/ `
x11+x12+x13+x14<=100;
3 o) {! }* k; C o' P/ D! m, Px21+x22+x23+x24<=120;
$ y, s4 ?; I4 j$ _$ {x31+x32+x33+x34<=100;
$ n$ U2 o$ y- F0 j4 [x11+x21+x31>=30;6 Z8 X# G3 i8 y) E, u; ~5 n# r' J
x11+x21+x31<=80; l1 F6 _) B3 z7 U
x12+x22+x32>=70;
) r$ E3 c" p, Tx12+x22+x32<=140;$ @5 j/ r8 h; D, i* t
x13+x23+x33>=10;0 w) e+ E3 e2 K- p9 C5 u
x13+x23+x33<=30;: J9 c( H) @8 }1 T5 Q% ~& G3 d
x14+x24+x34>=10;
' z! J; g& I G- P2 A* i3 M6 Zx14+x24+x34<=50;
7 U7 ]! P2 k) x2 S+ y+ s+ n6 Z9 \end; j+ q2 w# ?! e; Y" h4 o$ p
LINGO程序:
; E2 X" P4 F+ o( p) [" R; bmax=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;( y$ F+ b# t9 e
x11+x12+x13+x14<=100;
; a& `1 C+ ]6 jx21+x22+x23+x24<=120;
$ i9 c% _+ G E9 Z4 U+ Dx31+x32+x33+x34<=100;
) Q% n: l9 s' F; Q qx11+x21+x31>=30;! _0 v1 g4 Y* ]+ I
x11+x21+x31<=80;: ?( ] [- Q: W; Q7 l
x12+x22+x32>=70;$ j9 }( ~& N* i j" q" Y3 s7 p: a3 c
x12+x22+x32<=140;7 q. m6 d$ S6 `
x13+x23+x33>=10;
) b1 z; z2 C8 }" {* M& Zx13+x23+x33<=30;" h! {1 B3 F% z. E
x14+x24+x34>=10;
5 @& e& Q5 m% \; k" tx14+x24+x34<=50;7 T6 E! c9 N! |/ m
end" F* J8 |0 X- m! M
运行结果: + s5 h. f3 L+ U0 g6 ^( B
Global optimal solution found.
/ P) Z1 @, d" a, M% K Objective value: 88700.00
* l4 y( i. `+ X/ ?+ v0 G Total solver iterations: 7
0 H( w8 l" t3 c5 n" k! s% s3 `0 q
/ y' o1 M' h8 ^! {" C- W. p v1 q) X+ ?9 f
Variable Value Reduced Cost' a( t. ?! A- M& _ k; L2 T- W
X11 0.000000 20.00000
2 k7 Y0 D2 p. B. @" l$ ^8 e$ cX12 100.0000 0.000000) _% \* o5 c V7 Z& r- O, n# K" v
X13 0.000000 40.00000
# z1 l# Z. W" F1 X$ N4 UX14 0.000000 20.00000
" w/ W/ ?$ w& @* y% a+ rX21 30.00000 0.000000+ M( ~" p" `0 D5 R
X22 40.00000 0.000000
2 E5 H$ ?0 R3 _% Q/ N+ KX23 0.000000 10.00000
, }, b6 j H4 sX24 50.00000 0.000000
* K: t* i& m q( oX31 50.00000 0.000000/ v4 l( ]8 y" f
X32 0.000000 20.000001 D! S; m8 f5 }
X33 30.00000 0.0000002 C# y( H( y$ s$ m: G/ [
X34 0.000000 250.0000& M: q7 k) h: b( f
* [- H+ q( p1 g" o7 }) E- h& m9 iRow Slack or Surplus Dual Price
+ O# d1 O- R% x8 B$ K% e s1 88700.00 1.000000/ O- ~( H- L* ~1 w
2 0.000000 50.00000& h. U) A S m9 ]' {. l
3 0.000000 50.000003 [) I- J( s! {
4 20.00000 0.000000; s8 L9 O; n% r+ u' h
5 50.00000 0.0000001 e# o- U' R5 K5 Z9 K [& ?% v5 ]7 r
6 0.000000 260.0000
5 D- z) x0 Y' U% X5 {5 r7 70.00000 0.000000
1 c" i2 y: _ r6 H q! {8 0.000000 270.0000* h% w* Y$ }' ] v
9 20.00000 0.0000004 G9 k3 r7 d. A T
10 0.000000 220.0000
& t- F$ N+ j) T11 40.00000 0.000000
& O4 ] y( j4 K8 {3 h! @$ l1 F) S12 0.000000 250.0000 |
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