( )
! ( , ..)
: 1
2
3
4
5
1 <ENTER>
% 8
11
: GT% = 133,1639
1 ; 2
2 <ENTER>
Kn = 3720 (1 + 1,331639) = 8673,70
2
3 %. 1 3 ?
.
. :
,
- 1 3 :
.
.
:
.
DISCOUNT.EXE:
! ( , ..)
: 1
2
3
4
5
1 <ENTER>
% 3
15/3
: GT% = 11,7222
1 ; 2
2 <ENTER>
3
3 . . 4 70 % . 0,5 . .
1 :
= 70 %
= (1 + )1/12 1 = (1 + 0,7)1/12 1 = 0,04521 ≈ 4,52 %
q = P + 1 = 1,04521
:
.
:
1 ,
2 .
, .
, DISCOUNT.EXE:
! ( , ..)
: 1
2
3
4
5
1 <ENTER>
% 70
1/12
: GT% = 4,5211
1 ; 2
1 <ENTER>
! ( , ..)
: 1
2
3
4
5
2 <ENTER>
1
- ( - ).
% 4,52
48
6
% /A = 6,6286
|
|
% 285,0308
1 ; 2
2 <ENTER>
1
/ | |||
3,5 % | 127 . . | 3 | |
42 % | 570 . . | 5 | |
8 % | 1820 . . | 2,5 | |
38 % | 3720 . . | 3 | |
3,6 % | 735 . . | 5 3 | |
86 % | 530 . . | 1,7 | |
12 % | 8126 . . | 4 | |
6 % | 1274 . . | 1,5 | |
50 % | 2412 . . | 5 | |
16 % | 3207 . . | 1 4 | |
4 % | 896 . . | 4 2 | |
10 % | 17274 . . | 5 | |
45 % | 5120 . . | 3 | |
7,5 % | 715 . . | 1 3 | |
15 % | 7420 . . | 3,5 | |
48 % | 950 . . | 2 5 | |
6 % | 3247 . . | 3 | |
14 % | 346 . . | 1 7 | |
60 % | 20576 . . | 8 | |
11 % | 350 . . | 3 5 | |
16 % | 17760 . . | 11 | |
72 % | 1518 . . | 2 3 | |
7 % | 670 . . | 3 | |
18 % | 5520 . . | 7 | |
65 % | 2400 . . | 17 | |
9 % | 480 . . | 4,5 | |
14 % | 14000 . . | 1 4 | |
70 % | 8700 . . | 5 | |
6,5 % | 3450 . . | 5 7 | |
16 % | 960 . . | 2,5 |
2
/ | / | ||||
7 % | 2 | 7 % | 1 | ||
55 % | 3 | 74 % | 3 2 | ||
20 % | 7 | 11 % | 7 | ||
6,5 % | 1 | 5,5 % | 3 | ||
70 % | 4 | 10 % | 2 | ||
16 % | 1,5 | 65 % | 4 | ||
6 % | 13 | 8,5 % | 3,5 | ||
48 % | 2,5 | 15 % | 1 4 | ||
14 % | 1,5 | 82 % | 1 4 | ||
10 % | 0,5 | 7,5 % | 3 7 | ||
65 % | 5 | 18 % | 1 | ||
12 % | 1 | 63 % | 1 | ||
4,5 % | 3 | 4,7 % | 4 1 | ||
40 % | 8 | 11 % | 2 | ||
10 % | 5 | 57 % | 2 2 |
3
/ | |||||
7000 . . | 25 % | 3 | 0,5 | 1 | |
1500 . . | 32 % | 2,5 | 1 | 1 | |
20000 . . | 35 % | 4 | 1 | 0,5 | |
4700 . . | 20 % | 1,5 | 2 | 1 | |
1750 . . | 27 % | 2 | 0,5 | 1 | |
900 . . | 24 % | 1 | 1 | 1 | |
14100 . . | 27 % | 3 | 1 | 1 | |
45000 . . | 28 % | 5 | 1 | 1 | |
24200 . . | 32 % | 3,5 | 1 | 1 | |
9500 . . | 20 % | 2 | 1 | 1 | |
5500 . . | 30 % | 2,5 | 4 | 2 | |
2350 . . | 24 % | 1,5 | 2 | 1 | |
1500 . . | 30 % | 1 | 1 | 1 | |
47500 . . | 24 % | 4,5 | 0,5 | 1 | |
6930 . . | 35 % | 2 | 4 | 2 | |
12700 . . | 20 % | 3 | 1 | 0,5 | |
3200 . . | 18 % | 2,5 | 0,5 | 1 | |
10300 . . | 25 % | 3,5 | 3 | 1 | |
40000 . . | 17 % | 5 | 1 | 1 | |
15800 . . | 25 % | 4 | 0,5 | 1 | |
2000 . . | 23 % | 1 | 0,5 | 1 | |
4500 . . | 28 % | 2 | 0,5 | 1 | |
6350 . . | 25 % | 2,5 | 1 | 1 | |
30770 . . | 16 % | 4,5 | 2 | 1 | |
25000 . . | 23 % | 3,5 | 1 | 0,5 | |
11400 . . | 33 % | 3 | 1 | 1 | |
17700 . . | 17 % | 4 | 1 | 1 | |
55000 . . | 24 % | 6 | 1 | 0,5 | |
24000 . . | 19 % | 5,5 | 1,5 | 1 | |
8200 . . | 25 % | 2,5 | 0,5 | 1 |
|
|
2.
,
, n (j = 1, 2,, n). j - r i - ij (i = 1, 2,, r). q . k - j - ar + k , j (k = 1, 2,, q; j = 1, 2, , n).
:
.
r , r +1, ........, m (q = m r) .
:
b 1, ., br ( );
br +1,, bm .
xi, xi ≥ 0.
= ( 1, 2, , n).
:
11 1+ 12 2 + 1 nn ≤ b 1,
21 1+ 22 2 + 2 n n ≤ b 2,
r 1 1+ r 2 2 + rn n ≤ bn.
. :
w 1 = r +1,1 1+ r +1,2 2 + r +1, n n ≥ br +1,
wq = m ,1 1 + m ,2 2 + mn n ≥ bm, q = m r.
(1), :
1,1 1+ 1,2 2 + 1, nn ≤ b 1,
2,1 1+ 2,2 2 + 2, n n ≤ b 2,
r 1 1+ r 2 2 + rn n ≤ bn,
r +1,1 1 r +1,2 2 r +1, n n ≤ br +1,
m ,1 1 m ,2 2 mn n ≤ bm.
|
|
:
≤ ,
≥ 0.
, j - j :
: , .. , .
, .. .
-, . .
, , ( ). (, , ). .
, :
w 1 : w 2 : wq = k 1 : k 2 : kq.
, .
, .
k , , , :
j j - .
, :
.
:
f 2 = x 0 → max (f 2 = x 0 ).
, :
k 1 x 0 ar +1,1 x 1 ar +1,2 x 2 ar +1, n xn ≤ 0,
.
kmn x 0 am ,1 x 1 am ,2 x 2 am , n x 4 ≤ 0,
xj ≥ 0, j = 0, 1, , n.
, , . . .
, , . f 1 →max ( ) :
f 1 ≥ f 0 ( f 0).
. f 0 ≤ f *, f * .
, B , k 1 : k 2: k 3= a 1 : a 2: a 3.
:
- : , .
- .
- ( LINPROG)
- : , .
- ( LINPROG)
:
|
|
:
= ; = ; =(5; 2);
k 1 : k 2: k 3 = 3:2:2.
, .
, :
─ 6 1- , 4 2- 3 3- .
─ 1- , 7 0 3- .
3 , :
─ 2 1- , 4 2- , 1 3- ;
─ 3 1- , 0 2- , 2 3- .
b 1, b 2, b 3 ,
b 4, b 5, b 6 .
2 , c 1 , 1- , c 2 2- . k 1 : k 2: k 3 , .
- : 1, 2 . , :
(1)
: f = 5 1 + 2 2→ max
- :
, .. . , , .
6 1+3 2 = 18. , 1 = 0, 2 = 6, 2 = 0, 1 = 3, .. (0; 6) (3; 0).
6 1+3 2 = 18 . (0, 0) , 6 1+3 2 ≤ 18.
: 4 1+7 2 = 28, (0; 4)
(7; 0). 3 1 = 6, 1 = 2.
3, 4, 5 (1) ,
1 ≥ 0, 2 ≥ 0.
, (1). , 1 ≥ 0, 2 ≥ 0, D.
, f .
- f .
grad f = = (5; 2).
: f = const, :
5 1+2 2 = 0 : (0; 0) (2; 5).
-, , .
f. , :
6 1+2 2 = 18,
3 1 = 6, 1 = 2; 2 = 2, f * = 5 1 + 2 2 = 5∙2+2∙2 = 14 . .
, , , 14 , 2 1- 2 2- .
- - LINPROG.
- .
3 . : f 2 = 3→ max.
= ( 1, 2, 3) , , :
, .. .
- 3 , .. . - LINPROG.
x 1 = 1,71, x 2 = 2,57, x 3 = 3,43. (1,71; 2,57) BC .
. . . . --: , 1997. 320 .
:
1. = , = , = (5;7), k 1: k 2: k 3 = 3:4:2
2. = , = , = (5;4), k 1: k 2: k 3 = 4:2:3
|
|
3. = , = , = (4;2), k 1: k 2: k 3 = 1:3:2
4. = , = , = (1;7), k 1: k 2: k 3 = 3:1:3
5. = , = , = (5;8), k 1: k 2: k 3 = 4:3:2
6. = , = , = (2;3), k 1: k 2: k 3 = 3:2:1
7. = , = , = (7;12), k 1: k 2: k 3 = 4:4:3
8. = , = , = (4;6), k 1: k 2: k 3 = 2:3:2
9. = , = , = (3;2), k 1: k 2: k 3 = 1:3:2
10. = , = , = (1;3), k 1: k 2: k 3 = 3:2:4
11. = , = , = (1;4), k 1: k 2: k 3 = 1:3:2
12. = , = , = (2;4), k 1: k 2: k 3 = 2:3:1
13. = , = , = (4;6), k 1: k 2: k 3= 3:2:4
14. = , = , = (3;2), k 1: k 2: k 3 = 2:3:1
15. = , = , = (7;5), k 1: k 2: k 3 = 1:2:3
16. = , = , = (2;4), k 1: k 2: k 3 = 1:3:2
17. = , = , = (2;7), k 1: k 2: k 3 = 2:4:1
18. = , = , = (2;3), k 1: k 2: k 3 =3:4:1
19. = , = , = (4;6), k 1: k 2: k 3 =3:5:1
20. = , = , = (5;3), k 1: k 2: k 3 =1:3:2
21. = , = , = (2;6), k 1: k 2: k 3 =3:2:1
22. = , = , = (5;6), k 1: k 2: k 3 =2:4:1
23. = , = , = (3;4), k 1: k 2: k 3 =3:2:4
24. = , = , = (4;5), k 1: k 2: k 3 =3:5:2
25. = , = , = (3;4), k 1: k 2: k 3 =2:1:4
26. = , = , = (8;5), k 1: k 2: k 3 =4:3:2
27. = , = , = (2;3), k 1: k 2: k 3 =1:3:2
28. = , = , = (4;6), k 1: k 2: k 3 =2:4:3
29. = , = , = (5;4), k 1: k 2: k 3 =5:1:2
30. = , = , = (2;3), k 1: k 2: k 3 =1:2:3