Title: LINDO (Linear INteractive and Discrete Optimizer)
1????(?)
2- LINDO (Linear INteractive and Discrete
Optimizer) - ?? ?? ??? ?? ??? ????
Max. Z 40X1 30X2 s. t. 4X1 5X2
200 2X2 50 6X1
3X2 210 X1, X2 0
LINDO ????
3LINDO ????
4- LINGO ??? ??? ?? ? ?? ???? ??? ????
LINGO ????
LINGO ????
5- ?? ?? D????? 1?? ????? ?? ??
?????(portfolio) ???? - ????? ?????
???? ?????
A?? 7.3
B?? 10.3
M?? 6.4
N?? 7.5
? ? 4.5
6- ????
- ?????? 50??? ????? ???? ???.
- ?? ???? ??? ???? ???? 25??? ??? ??.
- B??? ?????? ??? ????? ??? ????? ? 60???
???? ???.
7- ???? (????? ????, ?? ??) X1 A??? ???
?? X2 B??? ??? ?? X3 M??? ??? ??
X4 N??? ??? ?? X5 ??? ??? ?? - ????(?????? ???) Max. Z 0.073X1
0.103X2 0.064X3 0.075X4 0.045X5
8- ????
- s. t. X1 X2 X3 X4 X5 10,000
(?????) X1 X2
5,000 (?????? ??)
X3 X4
5,000 (?????? ??) -0.25X3
- 0.25X4 X5 0 (???? ??)
-0.6X1 0.4X2
0 (B???? ???? ??) - X1, X2, X3, X4, X5 0
- ??? B????? ?? ???? ??? X2/(X1 X2)
0.6?? ??? ???.
9?? ? ???? ??? ??/????? ?????
X1 2,000 0 1 0 0.069
X2 3,000 0 2 0 0.022
X3 0 0.011 3 1,000 0
X4 4,000 0 4 0 -0.024
X5 1,000 0 5 0 0.030
????? ????? 800 800 800 800
10- ?? ????
- A??, B??, N??, ??? ?? 2,000, 3,000, 4,000,
1,000(??)? ??, - ????? 800?? (?? 8? ?????? ??)
11- ?? ??
- X3 0??, ? ????? 0.011 ? M???? ???? ?????
0.011?? ?? - ? ?? ???? ???? ?? 1,000 ? ?????? ????? 5,000??
1,000? ? ???? ?? ????? ?? - ? ?? ???? ???? ? 0.022 ? ?? ????? ?? ??? ??
?? ??? 0.022? ??? ?? ? ??? ?? - ? ?? ???? ?????? -0.024 ? ??? ???? ??? ?????
??? ??? 0.024? ?? ??? ?? - ?? ?? ?????? ???? ? 0.03
- ? B????? ?? ???? ??? ????? ?? 60??
(1/?????)?? ????? 0.03? ????? ??? ? ???
??
12- X1 ??? ???? ?? 0.018 0.103 ? A??? ?? ????
7.3??, ??? 1.8??? ????? 10.3?? ? ??? ????
??? ?? - ? ?? ???? ?????? ?? 3,750 10,000 ? ??????
??? ?? 3,750?? ????? 10,000?? ?? ? ??? ????
???????
13- ?? ?? E??? ???? ????
- ???? ??(???? ??)
??? ????? ??? ??????
??????? 9.0 1.0 2.5
????? 7.0 1.8 3.0
??????? 8.4 0.8 3.0
- ??? ??? 500??, ????? 1,200 ??, ?? ???? ? 600?
- ??? ??? ?????? ??? 100?? ???? ?? ??
14- ????(? ???? ??? ??) X1 ?????????? ????
X2 ????????? ???? X3 ??????????
???? - ????(3???? ???? ???)
- Max. Z 9X1 7X2 8.4X3
- ????
- s. t. X1 1.8X2 0.8X3 500
(??? ??) 2.5X1 3X2 3X3
1,200 (???? ??) X1
X2 X3 600 (???? ??)
X2
100 (????? ?????) - X1, X2, X3 0
15?? ? ???? ??? ??/????? ?????
X1 240 0 1 0 6.0
X2 100 0 2 0 1.2
X3 100 0 3 160 0
????? ????? 3,700 4 0 -7.4
16?? ???? ?? ?? ??? ?? ??
X1 9.0 7.0 10.5 1 420 540
X2 7.0 -8 14.4 2 1,100 1,500
X3 8.4 7.2 10.2 3 440 8
4 33.33 180
- ?????? ???????, ?????, ???????? ?? 240, 100,
100 ? ??? ???? ??, ? ???? ?? ?? ???? 240, 180,
80, ????(??)? 600, 300, 300 ??, ??????? 3,700??.
17- ?? ??
- ? ?? ???? ???? ? 160 ?? ??? 600-160 440?
??, ? ????? 73(440/600) ???? ???? ??.
18- ?? ??
- ? ?? ???? ?????(???? ????) 6 ???? 1?? ????,
???? 6??? ??? ??? ?? - ???? ?? ?? ???? 540?? ??? ??? ????? 6? ?? ???
?? - ???? 1,100???? 1,500????? ?? ????? 1.2? ??? ??
- ??????? ?????(?? 100) ????? ??? 7.4?? ?? ??
19- ?? ?? T????? ???? ?? ?? ?? ?? A, B? 1kg,
2kg ???? ?? 1kg ?? ???? ?? ? ????? 1kg? ??,
?????? ?? ?? ???? ??? ??? ???? ?? - 1. ??? ?? A? ?? 1kg? ???? ???? K? ????. 2. ???
?? B? ?? 1kg? ???? ???? M? ????. 3. ??? ??????.
- ? ??? ??kg? ?? ???? 2,100, ???? K? M? ??
-100, 150 - ????? ???? ??? 250?
- ? ??? ???? 5,000kg? 7,000kg
20- ????(?????? ??????, ?? kg)
- X1 ??? ??? X2 ???? K? ??? X3
???? M? ??? X4 ????? ??? ? - ????(???, ?? ?)
- Max Z 2,100X1 - 100X2 150X3 - 25X4
21- ????
- s. t. X1 0.5X2 5,000
(?? A? ??? ??) 2X1
0.5X3 7,000 (?? B? ??? ??) -X1
0.5X2 0.5X3 X4 0 (???? ??) - X1, X2, X3, X4 0
- ??A, B? ??? ?? ???? K? M? 1kg ??? ?? 0.5kg?
????? - ???? ?? ??? ???? ??? ??? ?(X1)? 3?? ????
???? ??? ?(0.5X2 0.5X3 X4)? ???? ???
22?? ? ???? ??? ??/????? ?????
X1 3,500 0 1 0 50
X2 3,000 0 2 0 900
X3 0 -175 3 0 -250
X4 2,000 0 ????? ????? 6,550,000
23- ?? ?? ?? A 3,500kg, ?? B 7,000kg?? ?????
3,500kg ?? ? ?? 3,500kg ?, 2,000kg? ????,
1,500 kg? ?? A? 11? ???? ???? K? 3,000kg
?? - ?????? ? ??? ??? ????, ? ????? kg? ?? 50??
900?? - ???? ??? ??? 1,400 ?? ?????, ???? M? ??? ???
325?? ??? ??? ???? ???? ? - ??A, B? ?? ??? ?? 5,000? 7,000??, ? ?? ??? ??
?? 50, 900? ????? ??? ? ???, ? ???? ? 7,000?
10,000???
24- ?? ?? M???? ???? ?? ?? ?? ?? ??
- ????? ?? ?????? ??
- ??? ? ??? ??? ?? ??? ??
- ? ?? ??? ?? ?? ??? ??
- 1000?? ??? ?? ???? ?? ??
- 1. ??? ? ??? ??? 400?? ??, 2. ??? ?? ??? ???
400?? ??, 3. ??? ???? ???? ??? ?? ??, 4. ??? ?
?? ? ??? 40? ???, 5. ??? ?? ?? ? ??? 60?
??? ???? ??
25? ? ??? ????
?? ?? ?? 2 2.5
?? ?? ?? 1.8 2
26- ????(? ??? ??? ???) X1 ??? ? ???? ????
????? ??? X2 ??? ? ???? ????? ????? ???
X3 ??? ?? ???? ???? ????? ??? X4 ??? ??
???? ????? ????? ??? - ????(??? ???, ?? ??) Min. Z 2X1
2.5X2 1.8X3 2X4
27- ???? s. t. X1 X2 X3 X4 1000
(? ??? ??) X1 X2
400 (1? ?? ??)
X3 X4 400 (2? ?? ??)
-X1 X2 - X3 X4 0 (3? ??
??) -0.4X1 0.6X2 0
(4? ?? ??) -0.6X3 0.4X4
0 (5? ?? ??) X1, X2, X3, X4
0 - ???, 4? ??? ?? ??? ??? ? ?? ? ??? ????
???(X2)? ??? ? ??? ? ??? ?? 40, ?, 0.4(X1
X2)????? ???, X2 0.4(X1 X2)? ???? ??
28?? ? ???? ??? ??/????? ?????
X1 240 0 1 2 3 4 5 6 0 0 -200 -40 0 0 -1.92 -0.28 0 0 -0.50 -0.20
X2 160 0 1 2 3 4 5 6 0 0 -200 -40 0 0 -1.92 -0.28 0 0 -0.50 -0.20
X3 240 0 1 2 3 4 5 6 0 0 -200 -40 0 0 -1.92 -0.28 0 0 -0.50 -0.20
X4 360 0 1 2 3 4 5 6 0 0 -200 -40 0 0 -1.92 -0.28 0 0 -0.50 -0.20
????? ????? 2,032 1 2 3 4 5 6 0 0 -200 -40 0 0 -1.92 -0.28 0 0 -0.50 -0.20
29- ????? ?? ?????? ??? 480??, ???? 520??,
?? ??????? ??? ?? ?? 400??, ?? ?? ??
600??? ???? ?? ???? 2,032?? ?? - 1, 4, 5?? ???? ???? ? ?? ??? ??? ?? ??
0.28(??), 0.5(??), 0.2(??) ? ???? ?? ??
????? ???? ?? ? ???? ??? ??? ??? ? ???
???? ??
30- ????? ??
- 1? ??? ??, ??? ?? ??? ?? ??? ??(?? 400)?
1??? ?? ??? 0.28? ??? ?????, ? ???? 500????
?
31- ?? ?? A??? ??? ?? ?? ?? 24?? ??, 8??? ??
?? ?? - ???? ?? ????
???(?) 2-6 6-10 10-14 14-18 18-22 22-02
????(?) 5 20 30 15 50 10
32- ????(? ???? ??? ???? ???? ?)
- X1 2?? ?????? ???? ? X2 6?? ??????
???? ? X3 10?? ?????? ???? ? X4
14?? ?????? ???? ? X5 18?? ?????? ???? ?
X6 22?? ?????? ???? ?
33- ????(? ??????? ???)
- Min. Z X1 X2 X3 X4 X5 X6
- ???? s. t. X1 X6 5 ( 2- 6 ????
???? ??) X1 X2 20 ( 6-10
???? ???? ??) X2 X3 30
(10-14 ???? ???? ??) X3 X4
15 (14-18 ???? ???? ??) X4 X5
50 (18-22 ???? ???? ??) X5
X6 10 (22-2 ???? ???? ??) - X1, X2, X3, X4, X5, X6 0
34?? ? ???? ??? ??/????? ?????
X1 5 0 1 0 -1
X2 30 0 2 15 0
X3 0 0 3 0 -1
X4 40 0 4 25 0
X5 10 0 5 0 -1
X6 0 0 6 0 0
????? ????? 85
3550
??????
? ? ? ?
40
??????
30
20
10
2
6
10
14
18
22
02
???
36- ?? ??
- ? ?????? ? 85?, ?????? ? 6-10???? 15?,
14-18??? 25? - 1, 3, 5?? ???? ?????? -1 ? ???? ??? ???? ??
1? ? ???? ????? (? ??????)? 1? ????? ?? ?? - 2, 4?? ???? ?????? 0 ? ????? ???? ?? ???? ?
????? ???? ??? ??
37- ?? ?? C??? ?????? ?? ????
- ??? ? ?????(?? ?)
? ? 4? 5? 6?
??A 2,000 5,000 3,000
??B 4,000 2,000 1,000
- 3?? ?? ??A, ??B? ???? 500?, 400??? 6?? ??
??? ???? ???? ????? ? - ?? ????? ??? ??? ???? ? 2,000?
- ?? 1?? ??? ??? ????? ?? 0.05??? 0.04??
- 3? ??? ?????? ?? 300??, 500??, 200??
- ?? ???(?? ??) ???? ???? ????????
38? ? 4? 5? 6?
??A 30 20 40
??B 20 15 30
- ? ??? ??? ????? 0.5? 0.4
- ???????? ????? ??? 0.3, ????? 0.2
- 3? ????? 5,000 ? ?? 3??? ????
39- ????(?? ??? ???, ???, ???????, ?? ?)
- X1, X2, X3 ??A? 4, 5, 6? ??? Y1,
Y2, Y3 ??B? 4, 5, 6? ??? IX1, IX2, IX3
??A? 4, 5, 6?? ??? IY1, IY2, IY3 ??B? 4,
5, 6?? ??? I1, I2, I3 4, 5, 6??? ??
??? D1, D2, D3 4, 5, 6??? ?? ??? - Ii ? Di? ? ??? ??? ??? ??? 0? ??? ??? Ii -
Di? ?? ? ???? ?? ???? ??
40- ????(??? ???, ?? ??)
- Min. Z 30X1 20X2 40X3 20Y1 15Y2
30Y3 0.5(IX1 IX2
IX3) 0.4(IY1 IY2 IY3)
0.3(I1 I2 I3) 0.2(D1 D2 D3) - ????
- X1 - IX1 1,500 (??A? 4? ??)
Y1 - IY1 3,600 (??B? 4? ??)
IX1 X2 - IX2 5,000 (??A? 5? ??)
IY1 Y2 - IY2 2,000 (??B? 5? ??) IX2
X3 - IX3 3,000 (??A? 6? ??) IY2 Y3 -
IY3 1,000 (??B? 6? ??) IX3 500
(??A? 6?? ???) IY3
400 (??B? 6?? ???)
41- ????
- X1 IY1 2,000 (4?? ???? ??)
IX2 IY2 2,000 (5?? ???? ??) IX3
IY3 2,000 (6?? ???? ??) 0.05X1
0.04Y1 300 (4?? ??????) 0.05X2 0.04Y2
500 (5?? ??????) 0.05X3 0.04Y3 200 (6??
??????) X1 Y1 - I1 D1 5,000 (4?? ????
??) X2 Y2 - X1 - Y1 - I2 D2 0 (5??
???? ??) X3 Y3 - X2 - Y2 - I3 D3 0
(6?? ???? ??) - ?? ??? ???
- ??? ???? ?? ????, ???? ???(Xi Yi)?? ? ???
???(Xi-1 Yi-1, 4?? ??? 5,000)? ?? ?? ?? ??
?? ?????(Ii - Di)? ?? ?? ???.
42?? ? ???? ??? ??/????? ?????
X1 1500 0 1 0 -30.0
X2 7000 0 2 0 -20.0
X3 1500 0 3 0 -20.5
Y1 3600 0 4 0 -15.5
Y2 2000 0 5 0 -39.8
Y3 1400 0 6 0 -40.3
IX1 1400 0 7 0 -30.2
IX2 1400 0 8 0 0
43?? ? ???? ??? ??/????? ?????
IX3 500 0 9 2,000 0
IY1 0 4.9 10 0 18.8
IY2 0 4.9 11 1,100 0
IY3 400 0 12 81 0
I1 100 0 13 70 0
I2 3900 0 14 69 0
I2 0 0.5 15 0 0.3
D1 0 0.5 16 0 0.3
D2 0 0.5 17 0 -0.2
D3 6100 0 ????? ????? 392,830
44 45?? 4? 4? 5? 5? 6? 6? ??
?? ??A ??B ??A ??B ??A ??B ??
????? 500 400 0 0 2,000 0 ?????
??? 1,500 3,600 7,000 2,000 1,500 1,400 2,000?
??? 2,000 4,000 5,000 2,000 3,000 1,000 3????
????? 0 0 2,000 0 500 400 5,000?
???? 75 144 350 80 75 56 ??????
?????? 300 300 500 500 200 200 ??A0.05
???? 81 81 70 70 69 69 ??B0.04
46- ????
- ????? ?? ???(9-11? ???)? ???? 0, 18.8, 0
5? ????(??? 2,000)? ??? ??? ??? 18.8?? ????
? ??? ?? - ????? ?? ????? ?? 0 ?? ????? 81, 70, 69???
???? ?? - ???? ???? (??? ??? ???)(??? ?? ??) ? ??
???? ???, 4? 5,100-5,000 100,
5? 9,000-5,100 3,900, 6?
2,900-9,000 -6,100 ???, ???? 0.3(100
3900) 0.26100 2,400 - ? ?? ?????(??A? 4? ??)? ???? -30 4? ???
???? ????? ??? ???? ??? 30 ?? ??? ???? ??
(?? 1400 3120)