, . x(ij) () , i, j (i 1 n, j 1 m). .
x11, x12xn,m () , 1, 2,..., n 1, 2,..., m . n*m . .
X:
x11 | x12 | x1m | |
x21 | x22 | x2m | |
xn1 | xn2 | xnm |
:
11 | c12 | c1m | |
c21 | c22 | c2m | |
cn1 | cn2 | cnm |
, , :
Z = c11*x11 + c12*x12 + + c1m*x1m + c21*x21 + c22*x22 + + c2m*x2m +
+ cnm*xnm
:
1.
i1 + xi2+... + xim, i, i, .
:
x11 + x12 + + x1m = a1
x21 + x22 + + x2m = a2
xn1 + xn2 + + xnm = an
, , j, bj, .
- :
x11 + x21 + + xn1 = b1
x12 + x22 + + xn2 = b2
x1m + x2m + + xnm = bm
, : xij, , , + , .
2.
, . : i < bj. , .
, , , , , , , .
:
x11 + x12 + + x1m = a1
x21 + x22 + + x2m = a2
xn1 + x n2 + + xnm = an
:
x11 + x21 + + xn1 <= b1
x12 + x22 + + xn2 <= b2
x1m + x2m + + xnm <= bm
3.
. , , . , p , , , , , .
|
|
n :
x11 + x12 + + x1m <= a1
x21 + x22 + + x2m <= a2
xn1 + xn2 + + xnm <= an
:
x11 + x21 + + xn1 = b1
x12 + x22 + + xn2 = b2
x1m + x2m + + xnm = bm
, , i. bj. .
1
, . (300, 100 250 ), , , , , .
, 200, 100, 150, 150, 50 . (.) :
9
, . .
1. Excel, .32. :
- 1.
- D19 :
= (C4:G6;C12:G14);
- Bi:
= (Ci:Gi)
- C7:G7
= (C4:C6): (G4:G6)
- C24:G27:
=C4*C12: G6*G14
, .
2. , .33, , .
3. , :
$B$4:$B$6 = $I$4:$I$6
$C$7:$G$7 = $C$9:$G$9
4. . .
.32
.33
2
, (300, 100 250 ) , 250, 150, 200, 150 100 .
3
, (300, 100 250 ) , 150, 50, 150, 100 25 .
, , , , , . , . , , , .
|
|
n 1, 2,..., n. 1, 2,..., n. , , , ( , , , ..). .
1, 2,..., n 1, 2,..., n., 1, 2,..., n . , .
, , ( ), :
∑ci*xi = ∑i*xi + ∑i,
xi , .
:
∑(ci-i)*xi = ∑i
, , , . (), . , , :
Z = ∑i*xi
, , :
Z = ∑ci*xi
:
∑(ci-i)*xi = ∑i
(), , , , .
1
3 :
- ;
- ;
- .
10.
10
1 , | , | , | |
50 000 60 000 55 000 | 5 000 6 000 5 500 | 10 000 000 15 000 000 12 000 000 |
, , . , 300 200 . , , , , 400 .
1. Excel, .34.
.34
:
, , 1 ( F4:G4).
F5:H7 10.
- H11 :
= (F4:H4;F5:H5)
- H14 :
= (F4:H6;F5:H6)
- L7:
= (F7:H7)
2. . 4 ( ). :
|
|
- D19:F19, , , :
=F5 - F6
=G5 - G6
=H5 - H6
- G19 :
=D19*F4 + E19*G4 + F19*H4
- I19 :
=L7
( G19 I19 )
- D20, E21,F22, :
=F4, =G4, =H4
- G20:G22, :
= (D20:F20)
= (D21:F21)
= (D22:F22)
3. , . :
- , .
- , .35, H11, F4:H4.
- , .35, .
- . .
- , . .
.35
- [1] [2] [3]. Microsoft Excel 2010. . .:, 2014. - 912 .
- .. Excel.- .: , 2007. - 240 .
3. Excel: - . . .. .: - , 2005.
[1]
[2]
[3]