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【1】求解:6 h8 u( `: a0 g: X. z
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:
4 q% E1 q5 V7 z& @% z3 c5 h( D1 i2 Fmax 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x33
& A$ y9 E2 z' }0 K* Qst
+ H$ M- W. B3 c& dx34=0;
1 c2 E0 n, @! c0 Ox11+x12+x13+x14<=50;
& N1 M+ \5 X2 w% jx21+x22+x23+x24<=60;
0 H2 q# o; }' b/ u; O* xx31+x32+x33+x34<=50;
/ r5 _. d5 d$ n3 @% c5 f g6 Ex11+x21+x31>=30;( l0 {4 w, w5 U4 T7 F& G( D/ f; z/ h
x11+x21+x31<=80;
0 X$ M" K" q+ e. g- rx12+x22+x32>=70;& O- c3 r- h+ k% s: T
x12+x22+x32<=140;
9 |; K; s' Y# C8 U" k0 Ix13+x23+x33>=10;
/ w1 X3 q* ], f* ?% B/ `x13+x23+x33<=30;3 j, b, U8 Y& S5 m
x14+x24+x34>=10;& X5 x5 m" Q; o( `8 ~+ D; @/ L
x14+x24+x34<=50;
0 k9 [1 Z5 q* d" l! g& a5 [end
/ ]3 S; j6 B: C+ o2 s- C6 p, xLINGO程序:; m, j" V" f/ M/ G& Y
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;/ Z5 M# r- Y1 K+ R; w
x11+x12+x13+x14<=50;; n/ ~* _5 y# I0 \* i
x21+x22+x23+x24<=60;
" r: [# s N) m1 k0 K' Vx31+x32+x33+x34<=50;& O& b. |8 f/ i+ J# t% Y7 X' t' R
x11+x21+x31>=30;
0 o% i& F2 N( wx11+x21+x31<=80;
7 R' X6 _) s, C: E0 R/ Px12+x22+x32>=70;. p9 g( H) ~. r0 E2 t; L9 x* R+ i H
x12+x22+x32<=140;
8 s" k: l" T& g, K$ k% ]! Px13+x23+x33>=10;
0 ?) a5 Z# x9 K( Y- v. v1 Y2 nx13+x23+x33<=30;
- H& N* @8 B) u. J% `' tx14+x24+x34>=10;
' e9 r# x- f' B- b3 I' k; o, ~x14+x24+x34<=50;; Y. E4 o, J+ [7 e
end6 i. ?8 S3 T- f3 {& q' f, z/ M1 M
运行结果:' _7 e/ Q1 Y! @, i
Global optimal solution found.# S" S% `! {6 k
Objective value: 47600.00
3 Y' B/ H. Y$ W) S, W Total solver iterations: 7
: a3 i2 E/ i9 l0 H% U/ j* h& P5 k, h
$ ^, i' O! r! f. u' c" z
Variable Value Reduced Cost' F3 v* r d1 j x1 l# a
X11 0.000000 30.00000
% E, p: ]; k9 [& y/ @X12 50.00000 0.000000
8 b2 Q3 F1 {1 h# }) Y9 i8 \X13 0.000000 50.00000+ U, N' p y0 `1 k! H! R& y
X14 0.000000 20.00000
j1 U! ?8 p6 h; B7 H3 \0 V! OX21 0.000000 10.00000
, r5 V* } F" i* |, OX22 50.00000 0.000000; ~) J! H& A9 u o9 N' U
X23 0.000000 20.00000; v8 T1 {& A' {0 [, R) H/ J- X' S
X24 10.00000 0.000000
/ C" [9 n7 Q5 f- `, G' r3 x( X7 CX31 40.00000 0.000000" Y0 L$ @0 v0 F2 B+ I7 R+ r
X32 0.000000 10.00000
! d, Q( C" x/ A" {1 M/ Z# v% HX33 10.00000 0.000000
4 A7 j5 j7 h5 E$ H ?; U8 h4 {X34 0.000000 240.0000
4 z; Y& K( u* n5 a3 ?9 x e, K+ d2 P/ B: h5 W. A
Row Slack or Surplus Dual Price
' P$ q7 o; m1 K' k: R1 47600.00 1.0000007 r. I4 M6 i$ E" o
2 0.000000 320.00000 j8 e7 y+ c2 R$ }7 k% j9 ]1 ~
3 0.000000 320.0000 o5 ~. z [& U( ?
4 0.000000 260.0000
2 L' O% t3 M- r1 k# ~5 10.00000 0.0000004 d9 h, m( B- Z/ y7 M
6 40.00000 0.000000
* t' ~ _( h# I; t4 ?% a! M2 @& K9 e7 30.00000 0.0000007 l3 Q' y9 P& r! f( X
8 40.00000 0.0000006 T$ p ~1 l6 ^- V2 U' G! U
9 0.000000 -40.00000+ Z: @9 V1 Q) J. [( G$ O- x
10 20.00000 0.000000
" Y9 ]: T1 F( A# `8 t1 p3 `, T8 y; G11 0.000000 -20.000005 F% \ y; k' c" Q" v( [% t) U
12 40.00000 0.000000
: z4 R; }' ^! d. \" v
8 q+ `; }4 S1 B" l- p% q) \2 U1 G【2】求解:
0 k6 w+ ]! Z/ r9 l. A c, Z模型:
7 n* u3 `. R6 ?0 |! V1 B4 ~4 u, Emax 290x11+320x12+230x13+280x14+310x21+320x22+260x23+300x24+260x31+250x32+220x335 d/ h- ?5 O& c2 ^5 P
st# t, O! ]$ H P
x34=0;( B/ T Z2 C% C, E" [6 q5 {
x11+x12+x13+x14<=100;
# ?' }% W! S0 z( v0 W+ n7 m; ^( @x21+x22+x23+x24<=120;6 l2 u) z$ @2 I. `5 c. c9 D
x31+x32+x33+x34<=100;! L" @+ E+ _1 U$ A6 Q
x11+x21+x31>=30;
$ A: `/ o7 c6 S6 h' dx11+x21+x31<=80;: [0 l* {2 M6 T3 e+ A2 u
x12+x22+x32>=70;1 ]* \* z3 d) r/ ]' V$ B& V! j
x12+x22+x32<=140;
+ F! J7 l1 {7 t0 n8 @- wx13+x23+x33>=10;& r6 X) i Y8 `1 E: O" R
x13+x23+x33<=30;* H3 c/ Z( m7 l
x14+x24+x34>=10;; a: h* z6 n" T3 S- h! X
x14+x24+x34<=50;
3 N7 P8 R. X0 ~) z8 Fend
+ U3 ]5 A* C9 N7 iLINGO程序:2 J* M6 t) i+ j% j5 \$ a. Z3 R
max=290*x11+320*x12+230*x13+280*x14+310*x21+320*x22+260*x23+300*x24+260*x31+250*x32+220*x33;
2 y' o r. U* t1 z2 W* P% {, [/ Yx11+x12+x13+x14<=100;
P3 ]0 E% `4 @x21+x22+x23+x24<=120;
2 L; E$ D% S7 E+ ex31+x32+x33+x34<=100;
9 V$ {, y2 D) Y `x11+x21+x31>=30;
- }7 j1 s3 S2 V U9 i3 t- Jx11+x21+x31<=80;2 ^1 w4 C7 j$ C: q& b V
x12+x22+x32>=70;; F1 A) F2 M5 } _& ^. z
x12+x22+x32<=140;" X2 ^4 ^: F' K& ~- r
x13+x23+x33>=10;( Q: N. F l2 |
x13+x23+x33<=30;2 I' ]# ^2 X3 t" D
x14+x24+x34>=10;
% c0 T$ Z6 v4 b9 Q: |. o- ]x14+x24+x34<=50;% ~( J: j2 f4 o& i
end( \( q+ u2 l: G6 L6 T K
运行结果: & {3 k( b5 Z# ?5 s6 Q; D: {
Global optimal solution found.2 V. T' g9 n! N
Objective value: 88700.00$ o7 J+ v0 I- E' R
Total solver iterations: 7
% F) z! I6 E0 ~; D" Z4 }, v. C% ^0 A# c% |% e+ e
, [, G# G( D9 q4 |4 q, l( X
Variable Value Reduced Cost% v: N U8 k6 @* t
X11 0.000000 20.00000
+ |9 R5 H) k* y, ^: YX12 100.0000 0.000000; `3 H& V% a$ x1 I' p, I
X13 0.000000 40.00000
. e) q# }2 Z3 Q P2 e1 @X14 0.000000 20.00000
; \1 A. N0 b* l5 [/ R* TX21 30.00000 0.000000
1 `% R; p- s8 ~X22 40.00000 0.000000# U5 J Z9 x7 m- s( e7 c$ L7 N% I
X23 0.000000 10.00000
9 |" ]6 R' C. w3 n6 U7 E! eX24 50.00000 0.000000) x+ a6 J# F; u9 F
X31 50.00000 0.000000, C9 e& l6 C% f9 V% c4 o- y. D
X32 0.000000 20.00000
# x% ~, Y! Q0 _X33 30.00000 0.000000
, W: n7 ]) }) \* z7 MX34 0.000000 250.0000
e; C5 k5 O, b2 G9 u3 t5 G
: ~; W( U: p) _* I' SRow Slack or Surplus Dual Price
! d' B9 U! G- I# n. o2 o1 88700.00 1.000000
6 \/ z, F, v0 H) {2 r: o. p2 0.000000 50.00000
4 ?; _2 y4 W! m3 0.000000 50.00000
7 V0 A* L8 O# x; j4 20.00000 0.000000
$ E' |1 r. B3 F5 50.00000 0.000000
' w8 W& p; Z$ \' i6 d9 H( L$ C6 0.000000 260.0000
" @/ A8 n( t% |' @9 b: N7 70.00000 0.000000
; F1 w2 b( {5 _" C8 0.000000 270.00003 A5 o& \7 S5 f$ u
9 20.00000 0.0000005 O1 J/ V8 d n" p; R
10 0.000000 220.0000
3 F. Q. m% ~! F' \* M11 40.00000 0.000000
$ `: }& L( u0 j12 0.000000 250.0000 |
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