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D8=. 2;>65=8O + 4518B. 704>;65==>ABL) / B5:CI85 ?0AA82K " (:>MDD8F85=B B5:CI59 ;8:284=>AB8) = B5:CI85 0:B82K/ B5:CI85 ?0AA82KB@0605B 4>AB0B>G=>ABL C ?@54?@8OB8O 45=56=KE 8 4@C38E A@54AB2, 4;O >?;0BK >1O70B5;LAB2 2 B5:CI89 <><5=B.2. =B53@0;L=K9 :>MDD8F85=B AB@C:BC@K :0?8B0;0 (IA:)IA: =  EMBED Equation.DSMT4 , 345:  (:>MDD8F85=B 02B>=><88) = A>1AB25==K9 :0?8B0; />1I0O AC<<0 2A5E A@54AB2 D8=0=A8@>20=8O $ (:>MDD8F85=B D8=0=A>2>3> ;525@8460) = 4>;3>A@>G=K5 >1O70B5;LAB20 + B5:CI85 >1O70B5;LAB20) / A>1AB25==K9 :0?8B0;  (:>MDD8F85=B 7028A8<>AB8 >B 2=5H=8E 709<>2) = (4>;3>A@>G=K5 >1O70B5;LAB20 + B5:CI85 >1O70B5;LAB20) / >1I0O AC<<0 2A5E A@54AB2 D8=0=A8@>20=8O%0@0:B5@87CNB AB5?5=L D8=0=A>2>9 =57028A8<>AB8 :><?0=88 >B :@548B>@>2.3. =B53@0;L=K9 :>MDD8F85=B @5=B015;L=>AB8 ?@54?@8OB8O (I@5=B) I@5=B =  EMBED Equation.DSMT4 , 345: ! (@5=B015;L=>ABL A>1AB25==>3> :0?8B0;0) = G8AB0O ?@81K;L/ A>1AB25==K9 :0?8B0; ! (@5=B015;L=>ABL >1>@>B=KE A@54AB2) = G8AB0O ?@81K;L / >1>@>B=K5 A@54AB20  (@5=B015;L=>ABL 8=25AB8F8>==>3> :0?8B0;0) = G8AB0O ?@81K;L/ (A>1AB25==K9 :0?8B0; + 4>;3>A@>G=K5 >1O70B5;LAB20)B@0605B ?@81K;L=>ABL 45OB5;L=>AB8 :><?0=88.  A;CG05, :>340 548=8G=K5 ?>:070B5;8 @5=B015;L=>AB8 8<5NB >B@8F0B5;L=>5 7=0G5=85  8=B53@0;L=K9 ?>:070B5;L B0: 65 1C45B 8<5BL >B@8F0B5;L=>5 7=0G5=85, GB> A2845B5;LAB2C5B >1 C1KB>G=>9 @01>B5 ?@54?@8OB8O.4. =B53@0;L=K9 ?>:070B5;L 45;>2>9 0:B82=>AB8 (I40) I40 =  EMBED Equation.DSMT4 , 345:  (:>MDD8F85=B >1>@0G8205<>AB8 4518B>@A:>9 704>;65==>AB8) = 2K@CG:0 >B @50;870F88/ A@. 4518B>@A:0O 704>;65==>ABL  (:>MDD8F85=B >1>@0G8205<>AB8 70?0A>2) = A515AB>8<>ABL ?@>4C:F88 / AB>8<>ABL 70?0A>2  (:>MDD8F85=B >1>@0G8205<>AB8 0:B82>2) = 2K@CG:0 >B @50;870F88 / A@. AB>8<>ABL 0:B82>2 >72>;O5B >F5=8BL :>=:C@5=B>A?>A>1=>ABL ?@54?@8OB8O 2 7028A8<>AB8 >B MDD5:B82=>AB8 8A?>;L7>20=8O A>1AB25==KE A@54AB2.II @C??0. >:070B5;8 >F5=:8 ?@>872>4AB25==>3> D0:B>@0 1. $>=4>>B40G0 ($>) $> = /!@, 345:  - >1J5< 2K?CA:0 ?@>4C:F88, BKA. @C1. !@ - A@54=53>4>20O AB>8<>ABL >A=>2=KE ?@>872>4AB25==KE D>=4>2, BKA. @C1.1>1I0NI89 ?>:070B5;L, E0@0:B5@87CNI89 C@>25=L MDD5:B82=>AB8 8A?>;L7>20=8O >A=>2=KE ?@>872>4AB25==KE D>=4>2.2. @>872>48B5;L=>ABL B@C40 (B) B =  /!!', 345:  - >1J5< 2K?CA:0 ?@>4C:F88, BKA.@C1. !!' - A@54=5A?8A>G=0O G8A;5==>ABL @01>B=8:>2, G5;.B@0605B MDD5:B82=>ABL 8A?>;L7>20=8O :04@>2 ?@54?@8OB8O.3. !515AB>8<>ABL 548=8FK ?@>4C:F88 (!54) !54 = ! / , 345: !  ?>;=0O A515AB>8<>ABL, BKA. @C1.  - >1J5< 2K?CA:0 ?@>4C:F88, "# %0@0:B5@87C5B B5E=8G5A:89 8 >@30=870F8>==K9 C@>25=L @01>BK ?@54?@8OB89, ?>:07K205B MDD5:B82=>ABL 8A?>;L7>20=8O 8745@65: ?@>872>4AB20 2 873>B>2;5=88 A>>B25BAB2CNI8E B>20@>2 8 CA;C34. >MDD8F85=B =5@02=><5@=>AB8 ?>ABC?;5=89 =0 A:;04 (=) == Qmax/QA@, 345: Qmax <0:A8<0;L=>5 ?>ABC?;5=85 3@C70 70 <5AOF, B>== QA@ - A@54=55 ?>ABC?;5=85 %0@0:B5@87C5B 8=B5=A82=>ABL @01>BK A:;040 8 ?>:07K205B MDD5:B82=>ABL @01>BK ;>38AB8G5A:>9 A8AB5<K ?@54?@8OB8O.III @C??0. >:070B5;8 >F5=:8 <0@:5B8=3>2>3> D0:B>@01.>MDD8F85=B MDD5:B82=>AB8 @5:;0<=>9 45OB5;L=>AB8 (@5:) @5: = (* )/  , 345:  (:>MDD8F85=B 87<5=5=8O >1J5<0 ?@>406) = >1J5< ?@>406 =0 :>=5F >BG5B=>3> ?5@8>40/ >1J5< ?@>406 =0 =0G0;> >BG5B=>3> ?5@8>40.    AC<<0 70B@0B =0 @5:;0<=CN 45OB5;L=>ABL =0 :>=5F >BG5B=>3> ?5@8>40, BKA. @C1.   - AC<<0 70B@0B =0 @5:;0<=CN 45OB5;L=>ABL =0 =0G0;> >BG5B=>3> ?5@8>40, BKA. @C1.>:07K205B AB@5<;5=85 ?@54?@8OB8O : ?>2KH5=8N :>=:C@5=B>A?>A>1=>AB8 70 AG5B C;CGH5=8O @5:;0<=>9 45OB5;L=>AB8.2. 5=B015;L=>ABL ?@>406 ( )  = ' / , 345: '  G8AB0O ?@81K;L >B @50;870F88 ?@>4C:F88, BKA. @C1.  - >1J5< ?@>406 ?@>4C:B0 ?@54?@8OB85<, BKA., @C1.%0@0:B5@87C5B AB5?5=L ?@81K;L=>AB8 @01>BK ?@54?@8OB8O =0 @K=:5, ?@028;L=>ABL CAB0=>2;5=8O F5=K B>20@03. >MDD8F85=B @K=>G=>9 4>;8 (  ) =/ , 345:  - >1J5< ?@>406 ?@>4C:B0 ?@54?@8OB85<, BC:    >1I89 >1J5< ?@>406 ?@>4C:B0 =0 @K=:5, BC:.>MDD8F85=B ?>:07K205B 4>;N, 70=8<05<CN ?@54?@8OB85< =0 @K=:54. >MDD8F85=B 4>2545=8O ?@>4C:B0 4> ?>B@518B5;O (!1) !1 = (*!)/ !, 345:  (:>MDD8F85=B 87<5=5=8O >1J5<0 ?@>406)= >1J5< ?@>406 =0 :>=5F >BG5B=>3> ?5@8>40/ >1J5< ?@>406 =0 =0G0;> >BG5B=>3> ?5@8>40. !  AC<<0 70B@0B =0 DC=:F8>=8@>20=85 A8AB5<K A1KB0 =0 :>=5F >BG5B=>3> ?5@8>40, BKA. @C1. ! - AC<<0 70B@0B =0 DC=:F8>=8@>20=85 A8AB5<K A1KB0 =0 =0G0;> >BG5B=>3> ?5@8>40, BKA. @C1.>:07K205B AB@5<;5=85 ?@54?@8OB8O : ?>2KH5=8N :>=:C@5=B>A?>A>1=>AB8 70 AG5B C;CGH5=8O A1KB>2>9 45OB5;L=>AB8.IV @C??0. >:070B5;8 >F5=:8 :>=:C@5=B>A?>A>1=>AB8 B>20@0 1. >MDD8F85=B ?@54?@>406=>9 ?>43>B>2:8 () = / , 345:  - AC<<0 70B@0B =0 ?@54?@>406=CN ?>43>B>2:C  - AC<<0 70B@0B =0 ?@>872>4AB2> ( ?@8>1@5B5=85) ?@>4C:B0 8 >@30=870F8N 53> ?@>406%0@0:B5@87C5B CA8;85 D8@<K : @>ABC :>=:C@5=B>A?>A>1=>AB8 70 AG5B C;CGH5=8O ?@54?@>406=>9 ?>43>B>2:8. 2. >MDD8F85=B C@>2=O F5= (#&) #& =( &max + &min)/2&C?, 345: &max  <0:A8<0;L=0O F5=0 =0 @K=:5,@C1 &min  <8=8<0;L=0O F5=0 =0 @K=:5, @C1 &C?  F5=0, CAB0=>2;5==0O ?@54?@8OB85<, @C1>:07K205B @>AB 8;8 A=865=85 :>=:C@5=B>A?>A>1=>AB8 ?@54?@8OB8O 70 AG5B 48=0<8:8 F5= =0 ?@>4C:B.3. =B53@0;L=K9 ?>:070B5;L :>=:C@5=B>A?>A>1=>AB8 ?@54?@8OB8O ?> :0G5AB2C (I:=) I:= = ";8= * "@07, 345: ";8=- :>MDD8F85=B :>=:C@5=B>A?>A>1=>AB8 ?> ?0@0<5B@C «;8=59=0O ?;>B=>ABL» ";8= = min / B, 345: B - 25;8G8=0 ?0@0<5B@0 «;8=59=0O ?;>B=>ABL» 0=0;878@C5<>3> B>20@0 min- <8=8<0;L=>5 7=0G5=85 ?0@0<5B@0 «;8=59=0O ?;>B=>ABL» A@548 2A59 0=0;878@C5<>9 3@C??K B>20@>2. "@07- :>MDD8F85=B :>=:C@5=B>A?>A>1=>AB8 ?> ?0@0<5B@C «@07@K2=0O =03@C7:0» "@07 = B / max, 345: B- 25;8G8=0 ?0@0<5B@0 «@07@K2=0O =03@C7:0» 0=0;878@C5<>3> B>20@0 max - <0:A8<0;L=>5 7=0G5=85 ?0@0<5B@0 «@07@K2=0O =03@C7:0» A@548 2A59 0=0;878@C5<>9 3@C??K B>20@>2. %0@0:B5@87C5B 7028A8<>ABL :>=:C@5=B>A?>A>1=>AB8 B>20@0 >B 53> :0G5AB25==KE ?0@0<5B@>2.! F5;LN CA>25@H5=AB2>20=8O <5B>48:8 >F5=:8 :>=:C@5=B>A?>A>1=>AB8 ?@54?@8OB89 ;53:>9 8 B5:AB8;L=>9 ?@><KH;5==>AB8 1K;0 @07@01>B0=0 0=:5B0 8 ?@>2545=0 M:A?5@B=0O >F5=:0 D0:B>@>2 :>=:C@5=B>A?>A>1=>AB8 ?@54?@8OB8O.  M:A?5@B=>< >?@>A5 ?@8=O;8 CG0AB85 254CI85 A?5F80;8ABK 20 ?@54?@8OB89 B5:AB8;L=>9, H259=>9, >1C2=>9 >B@0A;59 ?@><KH;5==>AB8 (  «@0A=0O =8BL»,  «!0;NB»,  «>;=0»,  «!525@=K9 B5:AB8;L»,  «!:>@>E>4»,  «8:B>@8O»,  «FOSP»,  «5@2><09A:0O 70@O»,  «0O:»,  «"@81C=0»,  «-;530=B»,  «20=B5:»,  «845@» 8 4@.)  E>45 8AA;54>20=8O M:A?5@BK >F5=8;8 ?> ?OB810;;L=>9 H:0;5 25A><>ABL :064>3> 87 G5BK@5E ?@54;>65==KE 3@C?? D0:B>@>2 >F5=:8 :>=:C@5=B>A?>A>1=>AB8 ?@54?@8OB8O, 0 8<5==>, :>=:C@5=B>A?>A>1=>ABL B>20@0, D8=0=A>2>3>, ?@>872>4AB25==>3> 8 <0@:5B8=3>2>3> D0:B>@>2. "0:65 1K;> ?@>2545=> @0=68@>20=8e >A=>2=KE ?>:070B5;59 >F5=:8 :064>3> D0:B>@0. ;O ?@>25@:8 AB5?5=8 4>AB>25@=>AB8 M:A?5@B=>9 >F5=:8 ?> :064>9 3@C??5 ?>:070B5;59 1K; @0AAG8B0= :>MDD8F85=B :>=:>@40F88 W, :>B>@K9 ?>:07K205B, =0A:>;L:> <=5=8O M:A?5@B>2 A>3;0A>20=K, B> 5ABL ?@8=04;560B : >4=>9 8 B>9 65 35=5@0;L=>9 A>2>:C?=>AB8 >F5=>:. >MDD8F85=B :>=:>@40F88 @0AAG8B0= ?> D>@<C;5:  EMBED Equation.DSMT4  345: 12 - ?>AB>O==0O 25;8G8=0 2 D>@<C;5 @0AG5B0 :>MDD8F85=B0 :>=:>@40F88, ?@54;>65==>9 5=40;;><; N  :>;8G5AB2> M:A?5@B>2; n  :>;8G5AB2> :@8B5@852 >F5=:8; ri- AC<<0 @0=3>2 i- 3> ?>:070B5;O; r- A@54=OO AC<<0 10;;>2 2A5E ?>:070B5;59. 5;8G8=0 :>MDD8F85=B0 :>=:>@40F88 <>65B <5=OBLAO 2 480?07>=5 >B 0 4> 1, 345 53> @025=AB2> 548=8F5 >7=0G05B ?>;=CN A>3;0A>20==>ABL <=5=89 M:A?5@B>2, 0 @025=AB2> =C;N A2845B5;LAB2C5B > B><, GB> A2O78 <564C >F5=:0<8 =5 ACI5AB2C5B.  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"01;8F0 3 - -:A?5@B=0O >F5=:0 25A><>AB8 D0:B>@>2 :>=:C@5=B>A?>A>1=>AB8 ?@54?@8OB8O @8B5@88 >F5=:8 M:A?5@B=0O >F5=:01234567891011121314151617181920$8=0=A>2K9 D0:B>@55445455555545555554@>872>4AB25==K9 D0:B>@423333233232223222330@:5B8=3>2K9 D0:B>@43424444333333434344>=:C@5=B>A?>A>1=>ABL B>20@054555555444454545455B>3>                    @>4>;65=85 B01;8FK 3      @8B5@88 >F5=:8!C<<0 10;;>2B:;>=5=85 >B A@54=53>204@0B >B:;>=5=8O 0=3>MDD8F85=B 25A><>AB8$8=0=A>2K9 D0:B>@951832410,40@>872>4AB25==K9 D0:B>@52-2562540,100@:5B8=3>2K9 D0:B>@69-86430,20>=:C@5=B>A?>A>1=>ABL B>20@0921522520,30B>3>30801238 EMBED Equation.DSMT4 = 0,62 !B5?5=L A>3;0A>20==>AB8 M:A?5@B=KE >F5=>: <>6=> AG8B0BL ?@85<;5<>9, B0: :0: W = 0,62 > 0,60 081>;55 7=0G8<K< A>3;0A=> <=5=8N M:A?5@B>2, O2;O5BAO D8=0=A>2K9 D0:B>@, 0 =08<5=55  ?@>872>4AB25==K9. @><5 B>3>, 2 48AA5@B0F8>==>9 @01>B5 CAB0=>2;5=K 2708<>A2O78 <564C ?>:070B5;O<8, E0@0:B5@87CNI8<8 :>=:C@5=B>A?>A>1=>ABL ?@54?@8OB8O. >AB865=85 :>=:C@5=B>A?>A>1=>AB8 ?@>872>48B5;5< 1C45B A>>B25BAB2>20BL 4>AB865=8N B0:>3> ?>;>65=8O, ?@8 :>B>@>< >= 8<55B >?@545;5==K5 2>7<>6=>AB8 @0728B8O, ?@>872>4AB25==K5 8 @K=>G=K5 ?@58<CI5AB20. 4=8< 87 8A?>;L7C5<KE ?>:070B5;59 045:20B=>AB8 C@02=5=8O O2;O5BAO :>MDD8F85=B 45B5@<8=0F88, =86=59 3@0=8F59 7=0G5=89 :>B>@>3> <>65B 1KBL ?@8=OB0 25;8G8=0 0,7. >;55 4>AB>25@=K9 @57C;LB0B ?@>3=>70 <>65B 1KBL 4>AB83=CB ?@8 1>;LH8E 7=0G5=8OE R (0,8-0,9). 0AG5B ?@>2>48;AO A ?><>ILN DC=:F89 MS Excel 87 :0B53>@88 «!B0B8AB8G5A:85»:  (@0AG5B ;8=59=>9 @53@5AA88). 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