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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:! w* }5 A6 _6 g ?; O ^ o8 P, @; j
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:
* u! Y# v+ O9 Q+ ]max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33. ]5 `, @% H {2 t g) m
st
. \0 I% ?0 @. |- ?x34=0;* v3 O, g W# J8 s
x11+x12+x13+x14<=50;1 W( s# o' ]) w h O% y% L5 i5 F
x21+x22+x23+x24<=60;$ e) U/ u* {& G; H
x31+x32+x33+x34<=50;1 b( J5 {( B- }4 W/ Z# ~7 p
x11+x21+x31>=30;
% d5 |: V/ W2 w4 c2 M8 J0 Bx11+x21+x31<=80;
3 z+ z+ ^. j i- M, Bx12+x22+x32>=70;
4 p A7 y" _9 ]4 K b3 px12+x22+x32<=140;
: H# G% @2 ]! ^% [6 u) B' R0 ex13+x23+x33>=10;8 O# \1 e, |4 @; h+ p$ o+ y) j7 j
x13+x23+x33<=30;0 b% S9 G% n6 V$ T/ ]8 Q
x14+x24+x34>=10;# u% n5 z9 X3 S/ i# Y
x14+x24+x34<=50;
- _5 g* q) Y1 Y c% |end
9 k, k2 m7 r8 C+ _) V$ J! ]( mLINGO程序:% s8 ]' m2 L& s2 l
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
; e" Z. S3 A" g7 ix11+x12+x13+x14<=50;! D# P" `* V, t. [
x21+x22+x23+x24<=60;
+ O, c& k& D9 o5 tx31+x32+x33+x34<=50;( Y# }8 ?$ Q, }1 S
x11+x21+x31>=30;
+ ]( o1 y! m) h2 ix11+x21+x31<=80;
+ q; n G; N% H# hx12+x22+x32>=70; k8 l: m5 _7 r- j$ i% O
x12+x22+x32<=140;. T5 R, H: k) B" @
x13+x23+x33>=10;
7 ?) ?2 A! G* P' [( n) hx13+x23+x33<=30;# C" V0 k: v m' v; g
x14+x24+x34>=10;1 G( m% l6 Q% A7 {
x14+x24+x34<=50;+ R% ^( h; z9 Z. ]1 O7 F* y! h
end8 u: I+ `$ F9 p4 @3 ?: \& H9 o
运行结果:7 \: R2 T7 e4 {5 p$ p
Global optimal solution found.
& E. j& t2 \/ G5 o0 e2 Z, D: T2 G Objective value: 47600.00
$ L! c: ^( Y: U @9 Z Total solver iterations: 7# p; `4 t l3 z) W0 Z
9 T4 f/ J$ l5 L1 @$ H
$ J4 O+ I7 W) L X& g
Variable Value Reduced Cost
- y, V' t K( m6 `X11 0.000000 30.00000
' \" g: g3 J8 x5 R( |5 h: ]6 l. DX12 50.00000 0.000000) f3 m' N1 E# r- z7 O
X13 0.000000 50.00000" J4 R( U1 S8 A# ?) x0 c9 Y
X14 0.000000 20.000009 R* S* p* c! Q; A3 `! D
X21 0.000000 10.00000
) ]5 j. M& q! ~X22 50.00000 0.0000006 w2 |/ @) E2 X1 Z% E
X23 0.000000 20.00000
- h( d: t6 b) pX24 10.00000 0.0000003 Z+ ~: l! z ]/ A z8 d
X31 40.00000 0.000000
3 }4 g3 c! s$ y, o. }X32 0.000000 10.00000: F- W# Z, C! U7 x6 f J' V' x5 u
X33 10.00000 0.000000
, ~& b3 Y. J8 S2 ? @+ B. zX34 0.000000 240.0000; }1 e0 ?. b; \: ^
, i& A7 N( N2 B& ~# Q& s
Row Slack or Surplus Dual Price9 t3 L5 N f# w' |3 o
1 47600.00 1.000000
r" k+ {! F5 M2 0.000000 320.0000
' Q. a, j5 C) {; e: @4 M" O3 0.000000 320.0000
7 }8 K" J# g! b4 0.000000 260.0000
) W% D$ [5 i, f+ Q5 10.00000 0.000000- g) E# ~. }: T- M% Y' C, F8 O
6 40.00000 0.000000
% N/ c9 H; ~4 P7 I4 k) _$ X" H7 30.00000 0.000000
9 N! x9 G. B) N5 ~- R) P. y8 40.00000 0.0000005 l! i! L1 O* E7 s9 y- h3 z p2 @
9 0.000000 -40.00000
2 G: M, E. y) C2 n7 G10 20.00000 0.0000009 m8 a# _& R- F, q, x1 t$ y
11 0.000000 -20.00000
; k7 v+ b$ \+ L' Q! k" \# b" m12 40.00000 0.000000& b! T, Y8 _( ^* [4 r0 E
9 Y! C+ E6 `2 ]' u8 u0 _4 d/ |6 `【2】求解:
3 h9 q) N) V: [4 `" i9 ^模型:
& I6 Z9 l- ~0 `( ~ {- V" i- smax 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
H2 K. [1 f, Qst. l9 \3 }) a+ `/ E- q" [+ W+ a' n
x34=0;: D, @# _- ~& Y
x11+x12+x13+x14<=100;- t1 @* z- u4 E7 y+ X1 z8 B" I
x21+x22+x23+x24<=120;
. I& U0 l+ C1 Rx31+x32+x33+x34<=100;5 ^2 ~) p4 J; ?2 l! k9 R( Y; t5 w
x11+x21+x31>=30;: f/ e V) v! t( n9 m% P
x11+x21+x31<=80;. a5 E O" z8 |) L* h: x* Z# c9 k/ R
x12+x22+x32>=70;" Q( B2 [! ?) k0 K0 n. l; J
x12+x22+x32<=140;9 j1 O1 o* @! C8 V
x13+x23+x33>=10;
& Z' `8 b& Z0 ox13+x23+x33<=30;4 g B* c0 W3 q9 |/ r
x14+x24+x34>=10;
. z- M; w; H( E, N2 i% Rx14+x24+x34<=50;
8 h: l; _7 p, S8 Uend
: W) `% L! g JLINGO程序:, |( H: G- i- i) a+ t y7 Z
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
. s' y$ A: n$ d7 w% f8 Px11+x12+x13+x14<=100;
; ?. J, m$ _& \! X* B& jx21+x22+x23+x24<=120;) X6 W* a) s {/ v% w/ u
x31+x32+x33+x34<=100;: O* G2 O. _/ s
x11+x21+x31>=30;
# G! G/ o2 Y1 E% y% M9 y& I) M- qx11+x21+x31<=80;
$ w& t# M9 @+ p4 r6 f5 e, Rx12+x22+x32>=70;
! g8 J; E1 i9 N+ [x12+x22+x32<=140;
, L [% g9 O4 ?! C* Y" A$ ^x13+x23+x33>=10;% r. J& {5 ?# U( L: C
x13+x23+x33<=30;$ o1 F' z& p/ p0 b& H: o! `
x14+x24+x34>=10;
' i/ i% f* I8 z8 U' E4 Lx14+x24+x34<=50;. g) `, @+ H1 O D
end+ n6 v3 e3 m! ]
运行结果: ) ` e( q1 M" X3 q% l$ i! ~
Global optimal solution found.2 Q7 @* c: b0 @( V
Objective value: 88700.00
3 A* D- l6 I) |9 G Total solver iterations: 7! {; f4 [% x7 `7 Y# B
3 u" c/ c: I9 i# g5 `. K# l- W9 v. R" W$ W, P! O
Variable Value Reduced Cost
) x) P' O0 G( _/ n- [* n1 f" GX11 0.000000 20.00000
* @) @% v) }4 w& eX12 100.0000 0.000000' T, v" m1 d. {, V# d
X13 0.000000 40.00000
# m1 @4 A% c# O" i7 nX14 0.000000 20.00000
8 Y: X W9 C1 j* w7 ^+ A) L: s5 zX21 30.00000 0.000000% A9 f" [) y6 [- W9 Z4 M
X22 40.00000 0.000000 D- Y6 t' O( ?/ f* F7 C' t' x
X23 0.000000 10.00000
# D3 X+ W. @" l, ]X24 50.00000 0.000000
3 r+ k7 Z/ h: @; tX31 50.00000 0.000000
+ D, |) r" G! v; |$ L0 G" mX32 0.000000 20.00000/ f5 A( W+ ~9 H! j
X33 30.00000 0.0000009 p$ E3 A/ C, F- |
X34 0.000000 250.0000+ W2 z/ ]; Z$ m6 P
3 @2 a9 T# Z7 q
Row Slack or Surplus Dual Price3 S6 T8 j j9 y7 [
1 88700.00 1.000000
: A! ~ R8 J. s7 b2 0.000000 50.00000+ A5 u. F5 @9 b! R& |* l0 Z
3 0.000000 50.00000
8 l0 X' l8 g/ H4 20.00000 0.000000
) Y4 E. A2 ~0 [# a3 J5 50.00000 0.000000- n8 P3 I. x3 D0 Z
6 0.000000 260.0000. W1 g% q8 c& Q( @- d* u2 D
7 70.00000 0.000000
9 E S2 G) a0 q. C0 z1 L* j( M8 0.000000 270.0000
/ @/ n4 P! H8 W g9 20.00000 0.000000
' p# k, C3 V; |; ~2 c10 0.000000 220.0000$ S6 N1 W+ ~" ]( M- M
11 40.00000 0.000000; m6 ~# o. L4 L/ A8 {6 W! H( g5 g; M
12 0.000000 250.0000 |
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