: , , .
, 1, 2,, n. U. 1, 2, , n. U = U (x 1, x 2,..., xn). , U → max. 1, 2,, n, D. p 1 x 1 + p 2 x 2 +...+ pnxn ≤ D. :
U (x 1, x 2,..., xn) → max,
x 1, x 2,..., xn ≥ 0,
p 1 x 1 + p 2 x 2 +...+ pnxn ≤ D.
.
7.1. , U (x 1, x 2, x 3) = . , 15, 10 15, 500. :
→ max,
x 1, x 2, x 3≥ 0,
15 x 1 + 10 x 2 + 15 x 3≤500.
Excel . 7.1:
7.1 7.1
4 =(B3*C3*D3) ( !), 5 =B3*B2+C3*C2+D3*D2. / . 4, . 3, 3 D3. , , .
5, ≤ D4. , 3, 3 D3 ≥ 0.
, , ʻ, : x 1 =11,1; x 2=16,7; x 3 =11,1; 45,4 (.7.2).
7.2 7.1
. , , . 5 15 x 2 . F , G . F1 , G1 . , 10 , x 2 =16,7. F7 10, G7 16,7. 11. 2 11, / , , . 3 x 2 =15,2. F8 11, G8 15,2. ( !) 2 12, 13, 14 15, F9-F12, , 3, ( , ) G9-G12. 10 . 2 5, 6, 7, 8 9, F2-F6, , 3, G2-G6. , , :
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F2 | F3 | F4 | F5 | F6 | F7 | F8 | F9 | F10 | F11 | F12 | |
G2 | G3 | G4 | G5 | G6 | G7 | G8 | G9 | G10 | G11 | G12 | |
33,3 | 27,8 | 23,8 | 20,8 | 18,5 | 16,7 | 15,2 | 13,9 | 12,8 | 11,9 | 11,1 |
. , (/), , ( ), .
G2-G12. ջ, F2-F12, . (.7.3).
7.3
.
. 200-500 50 , 3. H1 , I1 . 2 10, D4 200. . , 6,7. H2 200, 6,7 I2. , , D4 250, 300, 350, 400, 450, 500, 550, 600, H3-H10, , 3 I3-I10. 8,3; 10; 11,7; 13,3; 15; 16,7; 18,3; 20. , , . , (.7.3).
7.4
, .
7.1. U = U (x 1, x 2, x 3, x 4), p 1, p 2, p 3, p 4, D .
1. , .
2. , 5 , .
3. , 50.
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U (x 1, x 2, x 3, x 4) | p 1 | p 2 | p 3 | p 4 | D | U (x 1, x 2, x 3, x 4) | p 1 | p 2 | p 3 | p 4 | D | ||
ln(x 1 x 2 x 3 x 4) | x 3 x 4 | ||||||||||||
x 1(x 2+7) x 3 x 4 | x 3 x 4 | ||||||||||||
ln(x 1 x 2 x 3 x 4) | |||||||||||||
x 2 x 3 x 4 | x 1(x 2+1) x 3 x 4 | ||||||||||||
x 1 x 2 x 3(x 4+3) | x 1 x 2(x 3+5) x 4 | ||||||||||||
x 2 x 4 | x 1 x 2 x 4 | ||||||||||||
ln(x 1 x 2 x 3 x 4) | x 3 x 4 | ||||||||||||
x 1(x 2+7) x 3 x 4 | x 3 x 4 | ||||||||||||
ln(x 1 x 2 x 3 x 4) | |||||||||||||
x 2 x 3 x 4 | x 1(x 2+1) x 3 x 4 | ||||||||||||
x 1 x 2 x 3(x 4+3) | x 1 x 2(x 3+5) x 4 | ||||||||||||
x 2 x 4 | x 1 x 2 x 4 | ||||||||||||
x 2 x 3 x 4 | x 1(x 2+1) x 3 x 4 | ||||||||||||
x 1 x 2 x 3(x 4+3) | x 1 x 2(x 3+5) x 4 | ||||||||||||
x 2 x 4 | x 1 x 2 x 4 |
:
x 1, x 2, x 3, x 4 3-3. 4 :
1. =LN(B3*C3*D3*E3) 16. =(3*3)*D3*3
2. = B3*(C3+7)*D3*E3 17. =(B3*3)*D3*3
3. =(B3*C3*D3*E3; 0,33) 18. =LN(B3*C3*D3*E3)
4. =(B3)*C3*D3*E3 19. =B3*(C3+1)*D3*E3
5. =B3*C3*D3*(E3+3) 20. =B3*C3*(D3+5)*E3
6. =(B3*D3)*3*3 21. =(D3)*B3*C3*E3
7. =LN(B3*C3*D3*E3) 22. =(3*3)*D3*3
8. = B3*(C3+7)*D3*E3 23. =(B3*3)*D3*3
9. =(B3*C3*D3*E3; 0,33) 24. =LN(B3*C3*D3*E3)
10. =(B3)*C3*D3*E3 25. =B3*(C3+1)*D3*E3
11. =B3*C3*D3*(E3+3) 26. =B3*C3*(D3+5)*E3
12. =(B3*D3)*3*3 27. =(D3)*B3*C3*E3
13. =(B3)*C3*D3*E3 28. =B3*(C3+1)*D3*E3
14. =B3*C3*D3*(E3+3) 29. =B3*C3*(D3+5)*E3
15. =(B3*D3)*3*3 30. =(D3)*B3*C3*E3
x 1, x 2, x 3, x 4, x 2(p 2) x 3(D).
8
:
.
, .
.
:
1 | 2 | 3 | ||
1 | ||||
2 | ||||
3 |
1. , , .
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2. , , , 100, 150 200.
3. , 50%, 4 , 6 .
Excel.
1. F3 =(3:3) ( S). 124. F4 F5. 6 =F3-B3-B4-B5, 6 =F4-C3-C4-C5, D6 =F5-D3-D4-D5. . 3-D5 . 7 =B3/$F$3 ( $F$3 F3 F4). 7 8 9. 7 =C3/$F$4 8 9.
D7 =D3/$F$5 D8 D9. .
2. , , 100, 150 200, 3, 4 5. , Y = (E A) X. . 12 =, 11-D13
1 0 0
0 1 0
0 0 1.
(-). 16 (-)=, 15 =B11-B7. 15-D17. G3 ( ). : 1 B15:D17 ( -), 2 H3:H5 ( ). G3-G5 , , F2 Ctrl+Shift+Enter. .
3. 50%, 124,5, 4, 93, 6 , 138. G7-G9 124,5; 93; 138. X = (E A)1 Y. 16 (Ŗ) ., F15 ( ). B15-D17. F15-H17 F2 Ctrl+Shift+Enter. 7 . : 1 F15:H17, 2 G7:G9. 7-9 F2 Ctrl+Shift+Enter. . .
8.1. 4 .
xij Xj .
xij | Xj | xij | Xj | |||||||||
1. , , .
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2. , 2 , , , 10 .
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3. , 700, 500, 850 700.
, , .
1. .. - ( ). .: . 2010. 421.
2. .. . .: , 2005. 407.
3. .., .. : . 2- ., . . .: , 2006. 368.
4. .. : , , . .: , 2005. 208 .
5. : , (060000) / . .. , .. , .. . .: -, 2005. 351 .
6. .. : . 2‑ . .: , 2005. 616 .
7. .. , , : . . 2‑ . .: -, 2005. 287 .
8. .. . .: . 2006. 220 .
9. .. EXCEL. . - -, , 2004. - 242 .
10. Excel 2007. . ., .
-: , : DJVU, : 54,2008. - 448.
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