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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:# k( w1 _ T# u
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:
; h" M4 g" z; o$ umax 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33, ~4 O+ w) k9 n% S
st
7 M$ b% h* _" O1 r0 Y4 D9 zx34=0;0 R( E! k, P& f. N$ ~3 v
x11+x12+x13+x14<=50;
- t* }( r" M1 ~x21+x22+x23+x24<=60;
9 Y! T/ X( r# m) k7 mx31+x32+x33+x34<=50;/ J1 b0 M7 z1 v4 o
x11+x21+x31>=30;
) @% v6 C( P0 w( C+ s9 r: w( ~x11+x21+x31<=80;
) i0 S, F k% e% A. Y% }: Dx12+x22+x32>=70;
3 z8 A+ `# |0 b$ u1 a% \0 e6 yx12+x22+x32<=140;& P6 `! Z* F7 b0 Q+ S" b
x13+x23+x33>=10;+ O8 |6 X7 f) @
x13+x23+x33<=30;
1 ?% z" {2 Z: P5 i" t; R; H" Nx14+x24+x34>=10;
~2 s! d0 S1 _+ ^8 }' [- Xx14+x24+x34<=50;$ A9 ]) S+ Q9 }
end
! f% k0 Z$ B7 l* d4 I8 NLINGO程序:% x* d! u) u. u9 O3 D
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;% H" r4 u" [9 D' k
x11+x12+x13+x14<=50;
! Q' i! v! O0 F. X7 Z1 Tx21+x22+x23+x24<=60;
- k" n% L) y4 |* @, a* vx31+x32+x33+x34<=50;
4 W+ L6 t- ^' T9 q" T0 l$ q" `0 Gx11+x21+x31>=30;
7 J$ [( s: M" Z6 P+ c4 w0 @7 Qx11+x21+x31<=80;
9 n& W& a/ S3 }) f" s8 Cx12+x22+x32>=70;
) h5 k7 D5 L% p9 s+ N% px12+x22+x32<=140;, w) R% f7 C/ Q- n* h8 a
x13+x23+x33>=10;
D) ?8 j, i0 n" t! v8 |: Hx13+x23+x33<=30;. o" Z" G$ l5 K; ]9 s: b
x14+x24+x34>=10;' O3 y- @8 @* e2 D5 t# t& S
x14+x24+x34<=50;8 p* j5 J& e; L6 S ?2 M
end
8 q7 S0 f: m! w7 f }+ E运行结果:
4 c: l/ ^, L# A Global optimal solution found.2 r! V2 j7 K! ]8 B; G- Z2 n
Objective value: 47600.00' l6 @2 T+ k, a8 H& x
Total solver iterations: 7: @* r$ y0 @% G" i" ?+ X
5 B t0 g2 w5 b$ @* [9 H/ x
5 f" G+ W& T0 a7 @6 w( E K* \
Variable Value Reduced Cost" Z6 C7 o/ u+ y% W* W$ _: x
X11 0.000000 30.00000
0 q4 [ R1 R. i% y# o" P3 y- gX12 50.00000 0.000000# M0 r E% {+ J( J5 X, s
X13 0.000000 50.000000 \ s/ H( O$ I
X14 0.000000 20.00000
: ^! p3 B4 t/ a+ a, DX21 0.000000 10.00000
# b. p; c( @0 W& R( q3 DX22 50.00000 0.000000
+ U- `6 b j6 Q( cX23 0.000000 20.00000* P0 s. V! X7 U8 x3 s D* }
X24 10.00000 0.000000
& @. p" t4 ~# _X31 40.00000 0.0000001 Z- ]# J. w) \8 E; F
X32 0.000000 10.00000* [' C, x, F$ ^* y0 k5 y
X33 10.00000 0.000000
3 t4 }% m# t% n8 I( F* WX34 0.000000 240.0000
0 Q7 i2 B9 w. ^5 G; b9 H2 L* Z, ?& B4 n$ M% r3 D Y7 \/ ^$ F
Row Slack or Surplus Dual Price6 W; t) A( T Z0 g9 ]
1 47600.00 1.000000
+ R* u: C4 ~* B5 m' i0 d6 d# u* D2 0.000000 320.0000
, q) Y, @5 D% a+ Y& M$ ?0 V3 0.000000 320.0000
( O8 o. E$ e. ?4 b4 0.000000 260.0000 d! M9 ]" O1 o) D" y8 P7 C
5 10.00000 0.000000
+ [, [5 ^ G1 T; a/ c# m6 40.00000 0.000000
2 ?# u: k1 B" y9 e( ]7 30.00000 0.0000006 Y* ^4 R, J6 Z, c$ j/ E5 E' V
8 40.00000 0.000000
( F* l+ J& i/ ~ f# U% }, T" d& g0 z9 0.000000 -40.00000
* n5 B) M, `- N) J. t; _10 20.00000 0.000000
* a# Y0 m' B6 d11 0.000000 -20.00000
: R. W/ v% l# t12 40.00000 0.000000! \7 q7 j1 ^1 T# v9 x6 F
- C3 C% q; S* U【2】求解:
! L1 L) M* d; P) Q模型:
9 o9 X2 F ]8 h: u! Q; C Omax 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
8 C$ M/ n4 D+ \+ b- C; c2 Mst6 V3 V4 [9 w4 }- [+ F* s; Y
x34=0;% b% O/ a# `/ \) g- ~: z1 _
x11+x12+x13+x14<=100;1 a7 J4 n( v" v
x21+x22+x23+x24<=120;2 |0 m, I& p6 \3 p0 f
x31+x32+x33+x34<=100;
/ N1 t5 O4 y7 Y- mx11+x21+x31>=30;' ~ D0 p: `& X
x11+x21+x31<=80;
* b7 p3 P, p$ P$ O7 N9 K# k. h( hx12+x22+x32>=70;: f' @1 s* ?3 y4 k
x12+x22+x32<=140;
7 f7 a, l! {; Q0 T9 Lx13+x23+x33>=10;
+ g6 P# w4 N8 D) b& n1 Bx13+x23+x33<=30;2 F5 z/ U; s4 G2 F* y
x14+x24+x34>=10;3 D; Q9 P, A6 C' ?: V
x14+x24+x34<=50;8 q" D7 c+ R& z! m2 T
end
) M$ ~) m) h5 h! t c( [LINGO程序:5 `" k+ A9 }9 M; ^
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;; j$ p+ s6 {/ a' Y: P# e
x11+x12+x13+x14<=100;3 G5 @+ ~5 l' z
x21+x22+x23+x24<=120;: f& p3 R9 p/ h0 @8 s
x31+x32+x33+x34<=100;
* @0 ?5 ]: L6 G* Hx11+x21+x31>=30;+ A6 e7 I& R$ p# K7 k0 p
x11+x21+x31<=80;5 B/ `* X- q+ U* x
x12+x22+x32>=70;
/ D' {6 o4 \; L7 m2 \' q, Cx12+x22+x32<=140;1 M" U1 M/ S9 ^: n/ g
x13+x23+x33>=10;: M/ W! p$ \( @3 Z! ]9 y" ]
x13+x23+x33<=30;& M! w' C( C* W% o' j) P: \
x14+x24+x34>=10;" q+ t$ |6 p' e8 p% p4 Y7 j2 K
x14+x24+x34<=50;5 t2 ^/ \) B; S4 f5 ?1 t
end- @4 Q1 w/ P0 s* d; ]0 q5 e
运行结果:
( }! h9 H8 T3 C7 i L Global optimal solution found.+ {6 o, _' X( Y/ X1 q4 a
Objective value: 88700.006 \0 Q0 N6 B* z' _0 @9 T
Total solver iterations: 71 k) V1 ]1 V! {7 K
, s1 l$ }1 i) j# ^ X" x
& W' `$ w5 m7 J9 o7 y
Variable Value Reduced Cost
9 y; k" ~5 C; q) |7 }) X: q1 m' cX11 0.000000 20.00000
1 y. A$ ~. h# IX12 100.0000 0.000000
( y$ Y) P2 ]* f1 N( NX13 0.000000 40.000006 ^) t. i; l6 ]0 I6 O9 }. ?& T
X14 0.000000 20.00000. {" U/ V. D n* m
X21 30.00000 0.000000. `1 X: ` X4 w z& q: G Y' A
X22 40.00000 0.000000
, F- z0 J) [% WX23 0.000000 10.000008 u! m/ W" t# r, v
X24 50.00000 0.000000! E8 V: F, _" D: c% y! U9 Y) z
X31 50.00000 0.000000% T$ Z2 P4 w3 k3 g
X32 0.000000 20.000006 X+ |& W* K1 q$ l
X33 30.00000 0.000000
/ d N1 t, ]0 S; ?X34 0.000000 250.00004 R5 Y7 a6 m6 w7 B: k
( J% Z. D) S+ @( O& h1 J0 j0 O# k# }Row Slack or Surplus Dual Price
8 W( l8 l* ~- l9 [5 X8 b1 b1 88700.00 1.000000
( U+ w6 C$ I8 c7 f0 H2 ]6 H9 ?2 0.000000 50.00000' G( C4 I( j' B
3 0.000000 50.00000
, E1 @" d- t/ @6 F3 y+ C; d4 20.00000 0.000000' B% Q. f4 _: a f
5 50.00000 0.000000
& G! p' J. w6 G0 P: J6 0.000000 260.0000' |! c( _1 H E3 U
7 70.00000 0.0000006 e$ R. }; N6 u1 Z* `- q
8 0.000000 270.0000" a& o5 {8 d7 n( F/ A4 d! x( W% F
9 20.00000 0.0000006 d- U0 v" }, T% I( S
10 0.000000 220.0000
; T& w2 H2 w4 J% g, K' Y* Q5 X, u* k11 40.00000 0.000000& g6 s& I) ?4 f% q$ a
12 0.000000 250.0000 |
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