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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 f& \2 l0 u* t7 h2 U0 A$ G
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:
g8 |; l! y! D; M# o6 N x8 }& Imax 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
8 \' j. v# Y4 q: B7 Ust
$ e2 T$ M: _2 e' j+ Q+ V$ O. W3 ]* ix34=0;( F4 I* F$ {, D
x11+x12+x13+x14<=50;
; E5 v/ i; r: r$ E/ Ax21+x22+x23+x24<=60;
3 }( _: j b4 ^; ox31+x32+x33+x34<=50;
* Z( R) i( E" D+ _$ M: N% `. ^; Z. Hx11+x21+x31>=30;
/ g' H- T9 y, q* c. C: S+ sx11+x21+x31<=80;
4 W( H1 W5 n3 E: I" tx12+x22+x32>=70;' k! [9 y0 e% k7 @ X, v t( Z% c
x12+x22+x32<=140;
. p* S Z2 o M9 U" {) cx13+x23+x33>=10;' m1 ^$ K8 X! d. n2 w) W( w! }
x13+x23+x33<=30;: E, V4 J( @& `: \6 P# d% }$ y
x14+x24+x34>=10;
5 S/ ^4 Z [) h. `. ]. `x14+x24+x34<=50;
% |% o/ d" B; |( \, Kend
9 i; k/ J, R; h: X; Q# i FLINGO程序:
, v5 p5 z) E2 q5 U; qmax=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
4 N m( X7 U2 {; s% W3 _/ B9 Mx11+x12+x13+x14<=50;
, B( z3 U0 z9 l3 K/ ~% @9 y1 gx21+x22+x23+x24<=60;
' ?. [& K# M" D" ix31+x32+x33+x34<=50;
8 W6 J4 F; K, A' q2 ~x11+x21+x31>=30;1 R7 L5 E8 s5 e1 k7 y
x11+x21+x31<=80;9 r5 u: z: g. _) j g( h
x12+x22+x32>=70;
; o# T+ F: Q% T$ p0 ux12+x22+x32<=140;
0 r# x$ r* P+ gx13+x23+x33>=10;
, }* @0 l5 x! _, Z8 _9 [x13+x23+x33<=30;
+ N. R) [& T# W' \# A8 Ax14+x24+x34>=10;$ [; T$ N% Z# u. ]& N' N+ g
x14+x24+x34<=50; m+ c- l- l, A2 Q' a5 ]2 X
end8 y6 N' b7 {4 |) X( f, g, v% r! s+ n! s
运行结果:
0 O8 r9 b& Q" t/ R, ~- ~% U I Global optimal solution found.
! T& N& T( q/ v& V( [0 ` Objective value: 47600.00
q S4 [# F# |9 c) Y( b4 ^ [ Total solver iterations: 7* E3 o3 z* ~ Z4 W5 ]" e8 [* N
1 b( m! E: H) R) T
$ T- n1 M- U0 p2 GVariable Value Reduced Cost
$ Z5 v6 b# u3 N: MX11 0.000000 30.00000% W4 C/ M& S3 I1 y; N
X12 50.00000 0.000000
6 T5 d% f2 d. q2 y& v/ YX13 0.000000 50.00000+ r! c* a; M* j9 n$ O
X14 0.000000 20.00000
8 I0 u' i0 _& y( E% z a9 B) D% AX21 0.000000 10.00000
, T8 u: h3 g! ]8 o' f- ZX22 50.00000 0.000000
) x! J9 [" B0 H# c7 c8 u/ f! YX23 0.000000 20.00000
1 P: K3 e4 e' z8 f TX24 10.00000 0.000000
# W% m7 {7 l: _( u( u+ @; s0 W/ }X31 40.00000 0.000000
+ \9 n- k6 c: p/ y5 @X32 0.000000 10.00000( @5 p2 K2 R% {4 T- i% q
X33 10.00000 0.0000002 s' y( ?! O7 j0 j$ p8 X# p
X34 0.000000 240.0000
s( Q, r S) R0 L% E* d
0 a; d0 R% R. T0 _1 ?* a. I6 BRow Slack or Surplus Dual Price
5 h; `$ L+ n& ?4 f) b& r ]( d1 47600.00 1.000000" X8 I8 V1 _5 p0 Z S
2 0.000000 320.0000
4 w* n, J+ w: I! b1 A3 q. f3 0.000000 320.0000
; w& L8 }$ l) ]: c8 X+ [0 Z4 0.000000 260.0000
" A2 t" t# m: d! D* \) m, R. L5 10.00000 0.000000
- T6 [. P- D) |$ I! ]6 40.00000 0.000000
6 C/ [& a) [ q9 u! u+ |4 {' s7 30.00000 0.0000000 z3 O/ x. ^7 K7 n( [# e
8 40.00000 0.000000
5 i% c, h6 s4 ?) [( W9 0.000000 -40.00000
- X7 v, }( [: o a6 W4 g10 20.00000 0.000000' c% M9 N. I1 z$ v7 w+ `
11 0.000000 -20.000007 N6 b5 z( u& F
12 40.00000 0.000000 O+ | s2 N; h) |0 z# n
% P$ N. h" g" q. A' N( y$ t- C! n【2】求解:! S |3 f# a( D% V, Y
模型:3 s1 [/ g$ m8 z4 f; `' x* o8 P
max 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
( n* X2 @ V, }! @- r1 S1 V# m# T Sst6 T8 c7 U5 Q. q" t2 `, G6 E7 P( o
x34=0;. {; m# l! q6 H6 S* w- y+ e
x11+x12+x13+x14<=100;
# I/ [ f3 i! _7 `, B3 Q3 D' Tx21+x22+x23+x24<=120;5 P+ U( R6 N! m$ E+ y& ^7 p
x31+x32+x33+x34<=100;) l* v/ I: a% F' h5 f' ?' `4 a
x11+x21+x31>=30;* a- }: B2 ~! e( a% ]2 I$ `1 D
x11+x21+x31<=80;
/ s2 ^' P3 F9 E/ R4 Z$ gx12+x22+x32>=70;- t$ C; T2 C% l( w+ U( ]! u
x12+x22+x32<=140;0 W' M! h2 v |9 d# s5 z. w
x13+x23+x33>=10;; i- q' F0 ^+ X0 U1 P
x13+x23+x33<=30;; B9 n& c' ~' k, O. b. P
x14+x24+x34>=10;
1 p j; p5 \6 J7 Rx14+x24+x34<=50;
- {5 U$ j3 n0 a. a, r! k* w a" cend
0 X3 U/ v( A3 P9 w! x# j! |LINGO程序:( h2 x% ]( E8 ]7 n h5 \
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;4 F. I3 E& m4 |9 A
x11+x12+x13+x14<=100;
$ i5 j: }* g" H; u/ \x21+x22+x23+x24<=120;
/ g" |' d: u4 }8 b+ \x31+x32+x33+x34<=100; C5 w4 X* h4 a. l& R. E1 ?4 ?
x11+x21+x31>=30;
& I9 F- T6 V$ s& v* e3 Wx11+x21+x31<=80;. U2 u. M$ C2 p$ U4 c
x12+x22+x32>=70;. O% f9 e; a: k$ |8 T
x12+x22+x32<=140;
- e3 Z! b# X a5 G% u8 c1 Tx13+x23+x33>=10; ~$ k# Y; A; c3 Z8 B( }
x13+x23+x33<=30;
, Y3 K( P/ O) Z- X: sx14+x24+x34>=10;
, p: K! T! f M- d2 e4 i, q6 @x14+x24+x34<=50;; z, s8 E! n @+ \3 u
end
; w# W0 Y- I; E9 [运行结果: . \1 B! h; s, I4 {# p
Global optimal solution found.! Y9 u. l N; Y/ s
Objective value: 88700.00
: h& H. ^5 [" R Total solver iterations: 7
1 P j+ h: L6 D* W1 [+ V1 a$ @8 e* T4 G% s" K" {
* F; a' ]0 w, d6 `Variable Value Reduced Cost& O( U$ a7 O! Q% r
X11 0.000000 20.00000. S: m7 v# Y1 w* ~# N
X12 100.0000 0.000000
$ W4 u( w8 [, D0 O WX13 0.000000 40.00000
2 A- ]# \1 L4 G0 fX14 0.000000 20.00000* E" f+ A0 \. a
X21 30.00000 0.000000+ ]( s+ h2 g0 n7 a
X22 40.00000 0.000000
- }7 h. n* V4 H: NX23 0.000000 10.00000" L* u$ U1 Z) S1 e2 s! @+ _1 I
X24 50.00000 0.000000" r) L5 i: Q2 h# F7 D
X31 50.00000 0.000000
% g |9 g3 a* E+ y1 @( hX32 0.000000 20.00000
- l: U; D% T l1 \$ O0 P. l) EX33 30.00000 0.0000009 s* S8 ?* I# l
X34 0.000000 250.0000
2 f9 L0 q$ Y6 W- u ^ d3 ]0 ~7 d/ h
, A# I( M$ ?) g5 z* i* jRow Slack or Surplus Dual Price
8 s S a- U4 r1 88700.00 1.000000
" e4 y% Z- h& w/ P q2 0.000000 50.00000" m- [. `# t! ]! O) q/ Y
3 0.000000 50.00000
S. o: b: ^) `# u5 E' j. K: F4 20.00000 0.000000) c, E% T) C, T+ o7 w h
5 50.00000 0.000000
( |6 i1 K% O3 u7 a7 ^! u5 I6 0.000000 260.0000
, f2 O* r5 D. G+ a7 70.00000 0.000000$ h, o( _& g4 P# t
8 0.000000 270.00004 z$ h* u, Y/ A9 g* ]; V
9 20.00000 0.000000& u/ t, m' V( z, H3 D$ B6 t
10 0.000000 220.0000/ y+ i$ r, I* F
11 40.00000 0.000000
) l- S% w) f! i5 O3 j. F* |12 0.000000 250.0000 |
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