.


:




:

































 

 

 

 


, ( )

 

, - . , , . , , - .

-, , , , . , , , , . .

-, .

, .

. , , , , . . , . , , , .

 

:

-

-

- - -

녅..3

 

녅...14

 

19

25

 

腅26

 

28

 

1.1

:

  , .. , %(W)
1. 2 . 3. 4. 5. 6. 7.
  0,7              
, %              

 

 

1. ( ):

) :

i

*W= (. .) (1.1)

 

1. (): 700*0,2=140 . .;

2. (): 700*0,05=35 . .;

3. (.): 700*0,06=42 . .;

4. ( ): 700*0,35=245 . .;

5. (): 700*0,30=210 . .;

6. ( ): 700*0,03=21 . .;

7. ( ): 700*0,01=7 . .;

 

() . , ( ), .. .

 

, , .

 

:

i

*/100%= () (. .), (1.2)

.

1. (): 140*3/100%=4,2 . .;

2. (): 35*4/100%=1,4. .;

3. (.): 42*7/100%=2,94 . .;

4. ( ): 245*18/100%=44,1. .;

5. (): 210*12/100%=25,2 . .;

6. ( ): 7*10/100%=0,7. .;

7. ( ): 1*8/100%=0,08 . .

 

( ), 1 .

 

 

) :

=*I*n (. .), (1.3.)

n=2006.-2000. =6 ( );

I; 1,1( ).

 

1 = 140*1,09 = 152,6 ..

2 = 35*1,09=38,15 ..

 

3 = 42*1,09=45,78 ..

 

4 = 245*1,09=267,05 ..

 

5 = 210*1,09= 228,9 ..

 

6 = 21*1,09 = 22,89 ..

 

7 = 7*1,09 = 7,63 ..

 

, 6 6,6

 

) :

() = -

= *100%

 

=-/ =0

 

1=1/3*100%=33

2=1/4*100%=25

3=1/7*100%=14

4=1/18*100%=6

5=1/12*100%=8

6=1/10*100%=10

7=1/8*100%=12,5

1=140-0/33=4,2 ../

2=35/25=1,4 2 ../

3=42/14=3 2 ../

4=245/6=40,8 ../

5=210/8=26,25 ../

6=21/10=2,1 ../

7=7/12,5=0,56 ../

 

=- =6

 

1=4,2*6=25,22 ..

2=1,4*6=8,42 ..

3=3*6=182 ..

4=40,8*6=244,82 ..

5=26,25*6=157,52 ..

6=2,1*6=12,82 ..

7=0,56*6=3,362 ..

 

 

()1=140-25,2=114,8 ..

()2=35-8,4=26,6 ..

()3=42-18=24 ..

()4=245-244,8=0,2 ..

()5=210-157,5=52,5 ..

()6=21-12,6=8,4 ..

()7=7-3,36=3,64 ..

 

 

) .

 

()=

 

1=152,6/33*6=27,77

()=152,6-27,77=124,83

2=38,15/25*6=9,15

()=38,15-9,15=29

3=45,78/14*6=19,62

()=45,78-19,62=26,16

4=267,05/6*6=267,05

()=267,05-267,05=0

5=228,9/8*6=171,67

()=228,9-171,67=57,23

6=22,89/10*6=13,73

()=22,89-13,73=9,16

7=7,63/12,5*6=3,66

()=7,63-3,66=3,97

 

() , .. - . .

 

( ) 1- . 2- .

4 5 .

:

 

=/*100%, (1.6)

 

, 6 ;

.

 

=100/, (1.7)

.

 

4=100/18=5,5

5=100/12=8,3

 

:

 

4=244,8/245*100% =99,9%

5=157,5/210*100%=75%

 

, 6 , , .. 75%.

:

1=- (. .) (1.8)

 

1 = 245-267,05= -9%

 

1 = 210-228,9/210 = -9%

, 4 ( ) 9% . ., 5 () 9% . .

 

2- :

 

2= /- /, (1.9)

 

.

 

.

 

3. ( 0 :1. (); 2. (); 3. ().

1). :

2 , .

4=18%*2=36%

5=12%*2=24%

 

= - ∑)/100%* (. .)

 

= 1/*100%*2

 

 

4 : .. = 6, :

 

1 = 245*36%/100% = 88,2

2 = (245-88,2)*0,36 = 56,44

3 = (245-88,2-56,44)*0,36 = 36,12

4 = (245-88,2-56,44-36,12)*0,36 = 23,12

5 = (245-88,2-56,44-36,12-23,12)*0,36 = 14,80

6 = (245-88,2-56,44-36,12-23,12-14,80)*0,36 = 9,47

 

.. : 245+88,2+56,44+36,12+23,12+14,80+9,47. ., .. : 261,85-245 =16,85 . .

 

 

5:.. = 8, :

 

1 = 210*0,24 = 50,4

2 = (210-50,4)*0,24= 38,30

3 = (210-50,4-38,30)*0,24 =29,11

4 = (210-50,4-38,30-29,11)*0,24 = 22,12

5 = (210-50,4-38,30-29,11-22,12)*0,24 = 16,82

6 = (210-50,4-38,30-29,11-22,12-16,82)*0,24 = 12,78

7 =(210-50,4-38,30-29,11-22,12-16,82-12,78)*0,24 = 9,7

8 = (210-50,4-38,30-29,11-22,12-16,82-12,78-9,7)*0,24 = 7,38

 

.. 210+50,4+38,30+29,11+22,12+16,82+12,78+9,7+7,38= 239,39. ., .. 239,39-210 = 23,39 ..

 

 

2):

1/2 , .

 

4:

4 36%

1 = 88,2 . .

2 = 56,44 . .

3 = 36,12 . .

 

∑ 1/2 = 88,2+56,44+36,12= 180,76

=(245- 180,76)= 64,24 . .

4 = 5 = 6 = 180,76+64,24*3= 373,48 . .

 

 

64,24/247=21,41

 

5:

5 24%

1 = 50,4 . .

 

2 =38,30 . .

 

3 = 29,11 . .

 

4 = 22,12 . .

 

∑ 1/2 = 50,4+38,30+29,11+22,12= 139,93 . .

 

= 210-139,93 = 70,07

5 = 6 = 7 = 8 = 139,93+17,5*4= 209,93 . .

 

 

3):

, . , .

 

=

 

 

= (1.10)

 

 

=

 

i = Hi*K

 

4:

1 = (6-0)/(1+2+3+4+5+6)*100% = 28,5%

1 = 1* = 0,285*245 = 69,83 . .

2 = (6-1)/21*100% = 23,8%

2 = 2* = 0,238*245 = 58,31 . .

3 = 4/21*100% = 19%

3 = 0,19*245 = 46,55 . .

4 =3/21*100% = 14,3%

4 = 0,143*245 = 35,03 . .

5 = 2/21*100% = 9,5%

5 = 0,095*245 = 23,28 . .

6 = 1/21*100% = 4,8%

6 = 0,048*245 = 11,76 . .

 

∑ = 245 . ., .. , 6 2,45 . .

 

5:

1 = (8-0)/(1+2+3+4+5+6+7+8)*100% = 22,2%

1 = 1* = 0,22*210 = 46,62

2 = (8-1)/36*100% = 19,4%

2 = 2* =0,194*210 = 40,47

3 = 6/36*100% = 16,6%

3 =0,166*210 = 34,86 . .

4 = 5/36*100% = 13,9%

4 = 0,139*210 = 29,19 . .

5 = 4/36*100% = 11,1%

5 = 0,111*210 = 23,31 . .

6 = 3/36*100% = 8,3%

6 = 0,083*210 = 17,43 . .

7 = 2/36*100% = 5,5%

7 = 0,055*210 = 11,55 . .

8 = 1/36*100% = 2,8%

8 = 0,028*210 = 5,88 . .

 

 

∑ = 209,58 . ., .. , 6 .

 

:

 

 

1.2

, i I = 1-
4 5 4 5 4 5 4 5
1 122,5 105 88,2 50,4 88,2 50,4 69,83 46,62
2 122,5 105 56,44 38,30 56,44 38,30 58,31 40,74
3 122,5 105 36,12 29,11 36,12 29,11 46,55 34,86
4 122,5 105 23,12 22,12 21,41 22,12 35,03 29,19
5 122,5 105 14,80 16,82 21,41 17,5 23,28 23,31
6 122,5 105 9,47 12,78 21,41 17,5 11,76 17,43
7 - 105 - 9,7 - 17,5 - 11,55
8 - 105 - 7,38 - 17,5 - 5,88
735 840 228,15 186,61 244,99 209,93 244,76 209,58
½ 367,5 420 180,76 139,93 180,76 139,93 179,69 151,41

 

, :

1) 4 1/2 : 367,5 . . : 180,76 . ., 179,69 . .

2) 5 : 151,41 . . , .

, .

, , :

 

-

 

 

- max (1.11)

 

 

-

 

:

 

367,5-180,76 = 186,74 . .

420-139,93= 280,07 . .

367,5-179,69 = 187,81 . .

 

.

 

:

 

367,5-180,76 = 186,74 . .

420-139,93 = 280,07 . .

420-151,41 = 268,59 . .

 

367,5-179,69=187,81 . .

151,41-367,5=216,09. .

180,76-139,93=40,07. .

 

 

.

, , , .

 

4). ½ . () ( , ). (.) 5% , .. . = 0,05 .

 

= 0.05*0.675 = 0.033 (. ) 4

 

= 0,05*0,300 = 0,015 (. ) 5

 

4 : = 1/2 = 3

* , (1.12)

= 0,05*

 

675-498,052-0,05*675 = 143,198

= 675-364,5-0,05*675 = 276,75

 

5: = 1/2 = 4

= 300-216-0,05*300 = 69

= 300-144-0,05*300 = 141 . .

, , .

 

 

:

1.3

, . . ½
           
4 244,76 244,76 228,15    
5 209,58        

 

5., (, , ), :

) 30% 1 2 ;

) 30% 5 4 ;

) , 5 4 .

 

. , . :

 

) 30% 1 2 .

 

, , , , . , 30% , , , .

 

) 30% 5 4 .

 

, , , , 30% , , , .

). , 5 4 .

 

, . , - , , .

 

 

6). 1 . 35%.

 

ü :

 

(4.) = 122,5(. .)

(5.) = 105(. .)

ü :

 

(4.) = 69,83(. .)

(5.) = 46,62(. .)

 

:

 

ΔN = 35% (. .), (1.13)

 

ΔN ;

.; .

1- :

 

 

ΔN = 35% (69,83 122,5) = 18,43. /

 

ΔN = 35%(46,62 -42,62) = 1,4. /

 

ΔN = 18,43+1,4= 19,83(. ./) - ( ).

___ . ./ , , . .

 

.

2.1

:

  . ., . .       . . ., % t,  
1. 2. 3. 4. 5. 6. 7.
                   

 

.. = 90 . .

1.: ():90*0,20 = 18 . .

2.: ():90*0,35 = 31,5. .

3.: ():90*0,05 = 4,5 . .

4.: ():90*0,02 = 1,8 . .

5.: ():90*0,25 = 22,5 . .

6.: ():90*0,1 = 9 . .

7.: ():90*0,03 = 2,7. .

t .

 

 

... . . , : , , .

 

1. :

= ..*n(. ), (2.1)

n .

n = 365/t (), (2.2)

n = 365/24 = 15,21

= 90*15,21 = 1368,9 . .

 

, 1368,9 . .

 

2. :

). ():

t = 365/n

n = / = 1368,9/18 = 76,05 (2.3)

t = 365/76,05 = 4,80 (2.4)

 

, 4,80 , 4,80/24 = 0,2 20% .

 

) ():

t = 365/n

n = / = 1368,9/31,5 = 43,46 (2.5)

t = 365/43,46 = 8,40 (2.6)

 

, 3,6 , 8,40 /36 = 0,2 20% .

) ( ):

t = 365/n

n = / = 1368,9/(9+22,5) = 43,46 (2.7)

t = 365/43,46= 8,40 (2.8)

, 18, 8,40/36 = 0,2 20% .

 

) (, ):

t =365/n;

n = / = 1368,9/(4,5+1,8+2,7) = 152,1 (2.9)

t = 365/152,1 = 2,40 (2.10)

 

, 3,6 , 2,40/36 = 0,1 10% .

 

t = 4,80+8,40+8,40+2,40 = 24 ()

.

, : ( ). .. , , , , .

 

1. , 1,5 (t = t/1,5):

t = t/1,5 = 24 ;

n = 365/16 = 22,81 ;

t = 90*22,81 = 2052,9

= /n-/n 2052,9/22,81-2052,9/15,21 = 90-134,97 = -44,97..

(2.11)

 

 

, 1,5 , , .. , .

(2.12)

= /n-/n = 1368,9/22,81-1368,9/15,21 = 60,01-90 = -29,99..

 

, 1,5 , .. , , .

. 44,97 . ., 29,99 . ., . , , .

 

4. :

n =n-n; (2.13)

t = t/1.5 = 24/1.5 =16 () ;

 

n =365/16 = 22,81 (/) 1,5 .

:

n;=22,81 (2.14)

n=15.21-22,81 = -7,6 ()

:t = t-t

t = 24-16 = 8 ()

 

1,5 ( 24 8 ), 7,6 ( 24, 16) . 7,6 . , , .

 

5. , , :

a. 7 ( ), , .. , , , .

b. 6- ( ), , .. , , .

c. 7 5 , , .. .

5 6 ( ).

 

:

 

2.1

..

 

.   ( ) ( t)  
       
1. ,.. . .    
2. , . . 1368,9 2052,9
3. ,t    
4. ..,n 15,21 22,81
5. ..:      
-  
- -7,6
6. . . . . . - -44,97
7. .. . . - -29,99
8. .. :      
4,80 -
8,40 -
4,80 -
2,40 -

 

: 1) , ; 2) 8 , , 7,6 . . , , . , , .

 

  , / , /
     

 

 

1. ;

2. ;

3. = 0,5* = 0,05*140 = 7 . .;

4. = 0,005* = 0,005*140 = 0,7 . .;

5. () = 180,06/12 = 15 . .;

6. () = 0,5*456,3 = 6286,5 . .

228,15*5% = 11,41 . . , ..

228,15/12 = 19,01 = 11,41+19,01 = 30,42

7. . :

140*37% = 51,8 / = 0,0581../

8. ():

= 2*(*1,31+) = 2*(140*1,31+230) = 826,8 (./) = 0,83 ../

9. () ():

= 30%* (3.1)

 

1. .

 

:

, (*) (.+.*), :

. = -, . = 0

- =0, =

* = .+.*,

 

= (3.2)

 

. = 860 . ./.

= 0,39 /.

= 0,87 . ./.

, ./.

 

, :

 

= = 1792 (./.)

 

= .+*1 = 860+0,39*1792 = 1559 ../. (3.3)

 

1.

 

, , .. , , 1792 /. , , , .

2. , (30%* ). .

 

:

= 1559 . .

= 30%* = 1559*0,3 = 468 . . (3.4)

= = = 2767 . . (3.5)

= = +*1 = 860+0,39*2767 = 1939 ../. (3.6)

 

2.

 

, , 468 . ., 2767 ./. . .

 

3. ( ) :

 

1) 25%, ..

= 1,5*(*1,37+) = 1,5*(120*1,37+270) = 652 ./.

= =3282 ./.

= 860+0,39*3282 = 2140 . .

2) 50%:

= 3*(*1,37+) = 3*(120*1,37+270) = 13032 ./.

= = 942 ./.

= 860+0,39*942 = 1227 . .

 

3.

 

, 25% , , 1490 / 3282 /, 2140 . . 50%, 850 / 942 /, 1227 . . ( ).

 

4. ( .1) 50%:

1) ,

= 860*0,5 = 430 . .

= = 896 ./.

.. , 50% 896 /.

 

 

2) ,

= 270*0,5 = 135 ./. = 0,135 . ./.

= 0,12+0,135 = 0,255 . ./.

= = 1398 ./.

.. , ( 1398 ./.).

 

3) ,

= 120*0,5 = 60 ./

= 0,06+0,27 = 0,33 . ./.

= = 1593 ./.

 

.. , ( 1593 ./.).

.. , . .. 50%, 50%. 50%, 29%, 50%, 5%.

 

, ( ).

1) , :

- 50% , .1 ;

- .

 

4.

 

:

= 1,5* = 1,5*1792 = 2688 ,/ (3.7)

= 468 . .

= 860 . .

= 0,39 . .

= . . (3.8)

, , 884 ./., , 468 . .

 

2) , , :

- ;

- ;

- .

= 0,87 ../.

= 0,39 . ./.

 

= 468 . .

= 0,5*1792 = 896 ./.

 

5.

 

:

= -* = 1559-0,39*896 = 1210 . . (3.9)

.. , 1210 . ., , 468 . ., .

 

3) , , , :

= 1,5* = 1,5*1792 = 2688 ./ .;

= 860 . .;

= 0,39 . ./.;

= 3*(*1,37+) = 3*(0,12*1,37+0,27) = 1,3032 . ./.

 

6.

 

:

= -- ../ (3.10)

.. , 0,543 . ., , 468 . ., .

, , .

 

4) , , , :

= 0,87 ../.;

= 1792 ./.;

= 860 . .;

= 0,12 ../.

7.

 

:

= -- ../. (3.11)

.. , 0,01*1792 = 17,92 . .

( ), , .

 

 

, , :

3.2

. ( , =0) ( , =0,3* )
       
1. , . . .  
2. , , . . 0,12 0,12
3. , . . ./ 171,71 171,71
4. , .    
:      
- -- 14,3 14,3
- --    
- % -- 838,2 838,2
- -- 0,6 0,6
5. , . ./. 0,39 0,39
:      
- -- 0,12 0,12
- -- 0,27 0,27
6. , /.   -
7. /. -  
8. ./.    
9. , . ./. 1,56 1,94
10. , . ./ 0,70 0,70
:      
- --    
- -- 0,39 0,39
11. . ./ - 0,468
12. ./    
13. ./    
14. %    
15. %    

3.2 :

 

1) , , ;

2) 1792 ./.;

3) , 468 . ., 2767 ./.;

4) ;

5) 0, 0,468 . .;

6) , 169 ./.;

7) , 169./.;

8) , , :54% 12%.

 

, , , , .

 

:

1. = 140 ./.;

2. = 7 . .

3. =2543 ./.;

4. % (37%).

 

:

1. , :

=* = 0,12*2543 = 305,16 ../. (4.1)

= + = 6+305,16 = 311,16 . ./.

 

.. , 305,16 . ./., 311,16 . ./..

 

2. ():

1) : 1000 ./.;

2) : 1000 ./.;

3) : 1000./.;

4) : 550 ./.;

5) : 1000 ./.;

6) : 3000 ./.;

7) : 200 ./.

 

, = 1000+1000+1000+1000+550+3000+200= 7750./.

 

( 5500.), , .

 

 

 

:

1. = 860 . ./.;

2. = (-140,-230). ./.;

3. , : = 1792 ./.;

4. : = 2543 ./.

 

:

1. 3.2 ( 3) , () :

 

= (5.1)

 

, , ( 3.2: 480 ./., , , .. , 311./.), . .

2. , , . ( ) :

1 ;

2 , 1 ;

: ; /2; 2*.

 

5.1



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:


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, ; , .
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