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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:
6 y; g3 Z1 E! b Y. C; [! J4 j4 X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:# H1 {8 [4 i, s( C* x
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
7 M8 G" T5 Y* F: b7 W' N: Fst) V0 O+ @3 g1 s, z/ T6 c9 t. F
x34=0;
$ K2 b; L4 a& ]9 m0 cx11+x12+x13+x14<=50; O; }6 T, L) S
x21+x22+x23+x24<=60;) O( m4 ~0 Z4 _* l
x31+x32+x33+x34<=50;
; U) N) Z; b+ H8 m1 Cx11+x21+x31>=30;/ F9 E5 e; |- p- }1 q6 y( t
x11+x21+x31<=80;
) N0 y3 C$ d, V% F* v! {( `x12+x22+x32>=70;8 v$ R, Q: a% ]. t9 {
x12+x22+x32<=140;. G0 B* u, y. j7 P J
x13+x23+x33>=10;1 \' r# W8 K: \
x13+x23+x33<=30;
. H5 g/ S3 U, c# E9 Vx14+x24+x34>=10;1 w- Q, w. I( D* q. u8 Q
x14+x24+x34<=50;2 m4 |$ ]9 C# l M) R2 ^! ]4 ]
end0 f5 J; C# u! u) b6 ?' y
LINGO程序:/ ~2 D H: ~/ f! @7 N* c
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;- }3 s# E4 `6 H `7 `5 i
x11+x12+x13+x14<=50;
5 h3 ]2 m9 R+ X( Q' z6 ]" bx21+x22+x23+x24<=60;# D! _1 d; B: j& E1 o% H1 c- ?
x31+x32+x33+x34<=50; T) t% I. y$ L% M7 E7 v
x11+x21+x31>=30;8 l( g( e, J# J( _2 Y+ I; N
x11+x21+x31<=80;
9 q" r( y4 y9 J- Nx12+x22+x32>=70;
- K j3 D d7 S7 Px12+x22+x32<=140;
& d* z5 {' ?) ?; q# K2 j' |x13+x23+x33>=10;: j4 ^/ P1 [# ~( `* g; V! d
x13+x23+x33<=30;
# K+ |+ H7 w: Ex14+x24+x34>=10;
2 A# p) q3 h) y, lx14+x24+x34<=50;1 @- f; ]- P; S! {
end& d0 k# [. i: L' b( y3 d6 y
运行结果:
4 m+ L2 N; M7 D0 o Global optimal solution found.% R; S8 ?9 _& T1 f9 P
Objective value: 47600.00
# Y; @3 q4 V$ P# P Total solver iterations: 7
0 R u2 r6 r) O1 l* X; w1 C* K
5 ]8 V- d" }# E" s/ @: d$ s; Q* I
4 `% R ~$ U r6 f0 NVariable Value Reduced Cost. c; ], E7 }$ s2 u
X11 0.000000 30.00000+ H6 p! z- k& A% I5 v- w
X12 50.00000 0.0000007 U# P( p, ?) ?( t+ Q( p! V
X13 0.000000 50.00000! p& R- s5 v/ C' i4 L4 B1 F
X14 0.000000 20.00000. J/ i5 E* R! H/ [( |
X21 0.000000 10.00000
. p$ Y' ~+ m8 }( q# lX22 50.00000 0.000000
! J S* i3 k% S4 wX23 0.000000 20.000007 l, ]! R, e1 o" e, H2 K+ ?
X24 10.00000 0.000000% ]9 \- A8 b" y3 Z# S2 a& \
X31 40.00000 0.0000006 t' }! B: F+ B2 M3 u6 d
X32 0.000000 10.00000
, D, ^; @ @2 q. ~* {+ k# f# R- qX33 10.00000 0.000000; E" X% W" J) `! D9 V
X34 0.000000 240.0000
8 ]1 n8 Z+ n, a u( B' ^
+ Z. O# X8 S6 YRow Slack or Surplus Dual Price8 i6 M; w# J$ n; S1 q
1 47600.00 1.000000
$ L8 T% W6 {* M I0 K2 0.000000 320.0000
* B: p. c" e8 u% I1 ^. w3 0.000000 320.0000
- O: T/ o+ S0 @* U. G1 O4 0.000000 260.00005 K" L2 @4 A9 v+ D- |4 x0 z5 V
5 10.00000 0.000000
9 B8 G f+ _6 a! N- c6 40.00000 0.000000
6 y! z- u7 k8 {/ _2 u7 30.00000 0.000000
2 ]0 `& ]5 I8 U0 s' d8 40.00000 0.000000( ~# |0 G) y- Y# J, b6 J& y" n& l% {
9 0.000000 -40.00000
; v# T, s/ t p" D10 20.00000 0.000000
" t) u. z, H* G' p11 0.000000 -20.00000
. t1 m! n }* R12 40.00000 0.000000
' ]3 o3 D0 S0 Q1 N% K4 i9 F2 z! V1 M+ s
【2】求解:
8 U3 @5 H E4 g% @2 P9 n6 Z# k模型:9 K7 v, q' ^- E% K) b! T% L
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
: V1 o, v8 U2 b' u2 M, ?st- l/ X9 j* ]0 E. a! M9 U2 K
x34=0;4 `" f y# b7 J
x11+x12+x13+x14<=100;/ Z1 L& h4 X+ @5 ~
x21+x22+x23+x24<=120;
2 }1 Y; n6 T0 v) D S7 j5 K Rx31+x32+x33+x34<=100;- q! t$ A% r5 m0 k, P! q) C, M
x11+x21+x31>=30;- v8 o. y, M- y8 A
x11+x21+x31<=80;% T; r. S# V! ~, w
x12+x22+x32>=70;/ O, y4 A# U+ X* }) A. W8 L
x12+x22+x32<=140;
) ?: L# {/ |" |0 Z Nx13+x23+x33>=10;% R U% E4 E# @- V+ f' a
x13+x23+x33<=30;
8 Q6 [9 I* w; u1 T5 c4 _+ s1 S- wx14+x24+x34>=10;1 V9 x) N( y; r# v2 U
x14+x24+x34<=50;
8 E! S/ _: L- x, k9 fend
2 F; S( W( T" `/ O. ~4 {0 W: [LINGO程序:4 b6 J* O$ a* S9 U$ V# E
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
) P- R( `, T0 e3 v8 X/ J& Ix11+x12+x13+x14<=100;
9 ^+ ? S. ]" O5 B& M; @x21+x22+x23+x24<=120;
' O0 Q, F& K! ?) R% wx31+x32+x33+x34<=100;% a& f9 o, O' j' h; O4 S# T1 V
x11+x21+x31>=30;2 T" q" _9 P$ q2 l' b5 @, d) V& }7 ^
x11+x21+x31<=80;
+ B9 J' D2 x( s7 I7 E5 W! Qx12+x22+x32>=70;
$ U8 x, A r5 i1 ^9 Ex12+x22+x32<=140;9 Z" d& l7 {) a' @) {
x13+x23+x33>=10;8 X/ v. N3 Y1 r6 X0 m( m$ p
x13+x23+x33<=30;7 q; u! S* T4 u
x14+x24+x34>=10;
% H& e3 {$ t% B' J, O# o* x lx14+x24+x34<=50;
/ Q* L# g1 Z0 M6 n3 J+ _& F4 vend. R* I- X: c Z& q
运行结果: % W" X* Z; [8 m& I! J% P; f- R
Global optimal solution found.
& _, _% b& f# _ Objective value: 88700.00
m6 L: J8 ]9 i& i. p+ ~ Total solver iterations: 7( n7 G' P, e+ b5 u) s$ k
' x1 Q7 e1 {5 a
0 ]; w \) ~9 }) `$ \/ ?
Variable Value Reduced Cost) y- ]! P+ H! G# d4 T9 X* C- c
X11 0.000000 20.00000
2 a+ E+ Q% h: m" l7 vX12 100.0000 0.0000000 R. b0 d, `% @2 l- M& x* e( ]
X13 0.000000 40.00000
: C! R( {, G2 y; XX14 0.000000 20.00000
P' L! m! v& xX21 30.00000 0.000000: P2 K3 o2 m2 ?# ^
X22 40.00000 0.000000/ w* P& T* A1 W" c3 X
X23 0.000000 10.00000
7 ], A! `" D. S& s9 yX24 50.00000 0.000000
0 x c2 `" v& ~7 j! {X31 50.00000 0.000000- [6 k# R/ P8 g1 R- V s& \
X32 0.000000 20.00000
* F+ V' J) [' Q# y" |3 p/ H+ ?X33 30.00000 0.000000* L% _1 V/ F- R: \
X34 0.000000 250.0000; Y, X- o; [# M4 s: C9 ?
# { ]6 N1 S _! N5 o+ Z- TRow Slack or Surplus Dual Price
6 s) d4 K+ Q" L5 t1 88700.00 1.000000& g7 ]$ T2 X' \2 p$ o
2 0.000000 50.00000/ O3 j2 H- Z9 t+ S _* R6 R5 e' K: Q
3 0.000000 50.00000+ m: x8 h/ z' x) D8 S- B1 Q3 O# o
4 20.00000 0.000000
. Y" H! R) R' L7 M5 50.00000 0.000000
0 Z! W" B( _0 C. M6 0.000000 260.00004 P0 `! F+ W+ y( ?4 [8 }! y, L) z( y
7 70.00000 0.000000
9 m1 |$ d# ?9 w8 ?1 k4 K1 E8 0.000000 270.00009 K1 d9 Y4 G( B0 q! N/ K
9 20.00000 0.000000
5 e! J2 z/ ~4 W8 H10 0.000000 220.0000
6 _3 X! v8 N4 d11 40.00000 0.000000
; c7 l, o* q1 O; w" O1 W& T7 k3 s12 0.000000 250.0000 |
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