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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:
1 _! T7 D' {( |* Z' \: P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:
2 |5 Q. ^( k. ?$ m2 Lmax 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
6 R3 i7 E1 P6 X. ost. |3 n: B; J9 Q' G+ B' J
x34=0;$ ~) m% v* U$ D' S4 k- d& Q
x11+x12+x13+x14<=50;) A+ C" F( ~1 w+ |# A) M, o: \
x21+x22+x23+x24<=60;
3 ? e7 y( {7 b% l! L |: ]x31+x32+x33+x34<=50;/ M; A1 J' n% w( E
x11+x21+x31>=30;% P8 f: n5 z. K6 o- z1 t% m# \1 }, A
x11+x21+x31<=80;
( t9 X5 E) ^7 C# fx12+x22+x32>=70;
" A& C% C2 G' s2 g5 ex12+x22+x32<=140;
1 ^% W, y. R3 Z4 o/ P) {* fx13+x23+x33>=10;. |( e. Z6 J& o" }9 m# [
x13+x23+x33<=30;
2 H4 a8 S2 c2 hx14+x24+x34>=10;
/ Z, ~$ m6 ` t6 d# }x14+x24+x34<=50;' Z4 [+ d' k, }2 @7 \8 x9 k! Z
end
% m' i: Q4 N: N D0 oLINGO程序:, }3 _+ ~ x# ^- {6 @ |0 f
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;: T" U8 F" H: }3 g; K2 t
x11+x12+x13+x14<=50;* L1 r; _: S7 j# p7 L) j
x21+x22+x23+x24<=60;
5 }3 {" ^ o; N- {x31+x32+x33+x34<=50;- R: b9 c+ s# {5 q- N
x11+x21+x31>=30;
& a. a3 ^" Z$ [0 v' d% `8 jx11+x21+x31<=80;9 M9 r6 h U/ S7 y8 [
x12+x22+x32>=70;4 D. @; L8 H7 q
x12+x22+x32<=140;9 ^1 e# X) J: x v% L- B$ v8 z5 z
x13+x23+x33>=10;) J" ` t+ d$ I. p$ {
x13+x23+x33<=30;
# C- x) j' v" d) A7 }x14+x24+x34>=10;
# {( c- F0 r: q4 Mx14+x24+x34<=50;( M* q" K" L' R' I0 ]: _6 z& f
end
) I- z& l# d" o4 h- P# U运行结果:
5 H( R/ l1 _" Z& Z/ V: Y) Y Global optimal solution found.
2 R/ B, j2 G" F- _/ y; a Objective value: 47600.00
" j4 W1 \( A6 P+ { Total solver iterations: 7) n% _2 T q( u& Z# Y. n
' d( j0 t! d6 d) g; V: |3 V6 h
! e- F( F: [% a% K) _8 l
Variable Value Reduced Cost
2 L& h) v7 E+ G3 a( `! g5 CX11 0.000000 30.00000
5 a- r% ^- c$ H ^0 ]8 R: v7 IX12 50.00000 0.000000$ v! g" W! k( y7 v
X13 0.000000 50.00000; Q3 o1 z' p! p/ D
X14 0.000000 20.00000+ q' ]- v& f( ]1 g& ? @! }
X21 0.000000 10.00000
3 s/ e; Y( j- n( h/ _" Y) l0 }X22 50.00000 0.000000) f, [6 Z4 P) i! x" k( n x# ?
X23 0.000000 20.00000
0 R: H% q3 [9 u/ K( FX24 10.00000 0.000000
S: @5 Q8 R2 Y6 ?" p% UX31 40.00000 0.000000% ?) w3 C8 R6 D' f: M, {
X32 0.000000 10.00000
3 A! t2 c' y! j$ @' Y1 pX33 10.00000 0.000000# M1 _, O+ U0 p: d2 \% @" T7 w
X34 0.000000 240.0000
: D) Z) F0 n' `+ Q% v+ ~# S0 N" I* T3 K k
Row Slack or Surplus Dual Price
d* B; G- F5 Q' e3 `0 K7 G5 d0 I# P1 47600.00 1.000000/ U' V# e# ]: A5 ^, X: j
2 0.000000 320.0000$ C- Z% c; F/ p( v) ^) }5 z
3 0.000000 320.0000
( l# P2 X6 b# ~8 O% d4 0.000000 260.0000
* n" Q. u0 D* X8 |- K5 10.00000 0.0000006 D& D/ n" r6 Y5 N; w
6 40.00000 0.000000/ S+ b; M' p4 o, [& y4 {. Q
7 30.00000 0.0000009 o) T% f% ]0 g& Z0 a
8 40.00000 0.0000003 R. n W, z# o& S, m3 h
9 0.000000 -40.00000- x) y: U6 `$ I. B- m/ @
10 20.00000 0.000000
% ]& M; N' V& |/ N11 0.000000 -20.00000. L! S+ q; w3 `
12 40.00000 0.000000
4 b7 Z7 q3 `: d# o. w
6 d4 G8 H) B% \4 R9 n【2】求解:$ X& v8 y7 r3 R- Z" q# n
模型:1 v/ q+ a% V; r" c7 p* c
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x333 L) a& h% x3 N, c8 o/ C
st/ j! t4 y$ y# u( s0 q9 E
x34=0;
! c4 T( y0 g; O& }2 e. qx11+x12+x13+x14<=100;
" {% s' T: i* N) f3 B. N" m) Ix21+x22+x23+x24<=120;. f6 U, c% J1 r( V, S
x31+x32+x33+x34<=100;
4 f, O C6 l* d1 Q0 l# fx11+x21+x31>=30;
* _. f- W' L6 ~6 M% x) Gx11+x21+x31<=80;* m: o; [1 G; X, e
x12+x22+x32>=70;
& o/ }" g( d" P+ [% rx12+x22+x32<=140;* p7 Z8 @; `' W: L8 l7 }
x13+x23+x33>=10; ~; C+ b) D5 l B4 Q5 P
x13+x23+x33<=30;1 Q* h% g; K! F4 |. X" c F
x14+x24+x34>=10;2 P9 L, B$ H+ D- L- k* a7 m! L' i) F$ P K
x14+x24+x34<=50;
6 A3 V5 N4 }; u% F+ `7 V W4 y- {end! D* ^0 T$ J! ?( ?9 `
LINGO程序:+ e, [0 m' C( {& H, x$ |& b( Y3 e
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;. f2 R! r" N" }. y' N: X+ S% d
x11+x12+x13+x14<=100;
* O' x8 b# u3 D% }" v5 R2 f% v' }6 ix21+x22+x23+x24<=120;: }# `8 c# G' J, U6 s
x31+x32+x33+x34<=100;- z, a# G! x% ^- c
x11+x21+x31>=30;( }3 b' A# s- `" K$ |' i7 A/ w B/ _3 q
x11+x21+x31<=80;
7 Z- w+ i/ X* n! _$ Cx12+x22+x32>=70;
. v) p9 v* n- w8 k4 y9 A4 c2 K& tx12+x22+x32<=140;( Q0 U" C1 s4 t4 a
x13+x23+x33>=10;5 Y) e8 W- K+ T& L/ }
x13+x23+x33<=30;
/ n- q5 Z% c2 k* x" Sx14+x24+x34>=10;
) A1 E" R& [7 Qx14+x24+x34<=50;
( s& W- y' t1 v! Zend
( `9 `! s8 c/ s+ z H5 ~运行结果:
7 K. ^1 A: @- n, Q0 e Global optimal solution found.
# }& {* c- O$ W+ J( f4 B Objective value: 88700.00
# e) z1 s# q. J) F5 l0 o Total solver iterations: 7
1 x% r6 j5 h8 z! u' O
" T$ N( O; H# S( W0 q" e) L9 z6 v3 l4 a/ ^0 u8 n( g% a: K0 Y
Variable Value Reduced Cost' y' k, e; @, s
X11 0.000000 20.00000
% Y# W8 T" K' B0 o; c8 sX12 100.0000 0.0000002 p; d' i8 X* ~6 z2 g% _8 @. {& z
X13 0.000000 40.00000
: H7 F3 b. {" rX14 0.000000 20.000009 z; G% C" W/ E$ C8 P( y! u: A7 ]
X21 30.00000 0.000000
( j1 b5 _1 l3 }X22 40.00000 0.000000" o2 r9 x1 @( c! V/ F
X23 0.000000 10.00000
, w' l* {( {4 R, `) mX24 50.00000 0.000000+ U% J# F5 H% G4 C
X31 50.00000 0.000000
+ J* g$ d# {( H, x/ OX32 0.000000 20.000001 }( |7 B" K# W) \
X33 30.00000 0.000000
7 i8 O) E0 h$ }9 z( U w ~- u! IX34 0.000000 250.0000! |) s0 r b8 ?( ^9 X; \. h
3 @- D( M( Y; p$ o3 A: ?) h
Row Slack or Surplus Dual Price. a1 j9 ?6 M! Q( K9 C Z
1 88700.00 1.000000
2 Z+ |) @5 U e2 0.000000 50.00000
0 U0 D/ u: s2 b, C5 R2 a- l$ @3 z/ f2 l3 0.000000 50.00000) U* B: R! B8 a+ Q* T' K
4 20.00000 0.000000. L( A# T* ?$ z! k" ~
5 50.00000 0.000000- Y: d: j7 P$ ?; m' a
6 0.000000 260.0000
2 d. v: F$ C! {% |+ A! t& t7 70.00000 0.000000
2 P9 `7 u& M0 o9 l" t, {4 ]/ |$ j+ G8 0.000000 270.0000
3 u8 |/ j6 L- k1 h1 D3 z% r9 20.00000 0.000000 E, z, R& a2 c! l( f
10 0.000000 220.0000
; `5 L/ m( P- T1 q8 W$ `11 40.00000 0.000000
4 r% i1 w5 T7 ]12 0.000000 250.0000 |
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