DL Balance

8/18/2019 DL Balance

1/19

Microsoft Excel 15.0 Answer Report

Worksheet: [Mander.xlsx]Sheet1

Report reated: !"!"#015 11:0$:1$ AM

Res%lt: Sol&er fo%nd a sol%tion. All onstraints and opti'alit( conditions are sati

Sol&er En*ine

Engine: GRG Nonlinear

Solution Time: 0.016 Seconds.Iterations: 0 Subproblems: 0

Sol&er +ptions

Max Time nlimited! Iterations nlimited! "recision 0.000001

#on$ergence 0.0001! "opulation Si%e 100! Random Seed 0! &eri$ati$es #entral

Max Subproblems nlimited! Max Integer Sols nlimited! Integer Tolerance 1'! (ssume N

)b*ecti$e #ell +Min,

ell ,a'e +ri*inal -al%e inal -al%e

--/ sum o suares /.2363242E501/ /.2363/E501/

ariable #ells

ell ,a'e +ri*inal -al%e inal -al%e /nte*er

-7-3 8e 9 20 20 #ontin

#onstraints

ell ,a'e ell -al%e or'%la Stat%s Slack

-7-4 c 9 0.4 -7-4;1 Not 7inding 0.2

-7-4 c 9 0.4 -7-4


2/19

)ed.

onNegati$e


3/19

Microsoft Excel 15.0 Sensiti&it( Report



ariable #ells

inal Red%cedell ,a'e -al%e radient

-7-3 8e 9 20 0

#onstraints

inal a*ran*e

ell ,a'e -al%e M%ltiplier

-7-4 c 9 0.4 0

-7-4 c 9 0.4 0


4/19

Microsoft Excel 15.0 i'its Report



+23ecti&e

ell ,a'e -al%e--/ sum o suares /.2363/E501/

-aria2le ower +23ecti&e 4pper

ell ,a'e -al%e i'it Res%lt i'it

-7-3 8e 9 20 0 2.=/>?3E5010 2=


5/19

+23ecti&e

Res%lt

1.?//=3E5011


6/19

@d 9 x 8Ae del"S delBd sum

4 = 0 20.2/41 0 0 0

0.01 20.2/41 54.6/604E5004 3.142?4E5004 51.=E5004

@lC2 200 0.02 20.2/41 50.000000131 1.?/=6?E5003 52.3E5004

E 2>000 0.0/ 20.2/41 52.=/4?>E5003 2.1=1/=E5003 5/.>E5004

I 1000 0.0? 20.2/41 50.000000//= 2.46?==E5003 5?.>E5004

8e 20.2/41 0.0= 20.2/41 5?.1?/=4E5003 /.=3???E5003 5=.3E5004c 0.40>=2? 0.06 20.2/41 50.000000?>2 0.000000?24 56.?E5004

c in$ 1.2/=2>? 0.03 20.2/41 5=.63444E5003 ?.>4114E5003 53.0E5004

0.04 20.2/41 50.0000006?2 =.636=1E5003 53.?E5004

sum o suares 0.0> 20.2/41 53.1???0E5003 6./6=?>E5003 53.4E5004

2.>/E501/ 0.1 20.2/41 53.4=0>>E5003 3.0?3?1E5003 54.0E5004

sum o deD. 0.11 20.2/41 50.0000004=? 3.321=4E5003 54.2E5004

51.3E5006 0.12 20.2/41 5>.21142E5003 4./43/1E5003 54.2E5004

0.1/ 20.2/41 5>.46603E5003 >.0?/>?E5003 54.2E5004

0.1? 20.2/41 51.0=02>E5006 >.6>042E5003 54.1E5004

0.1= 20.2/41 51.11222E5006 1.0/23/E5006 53.>E50040.16 20.2/41 51.132?1E5006 1.0>=24E5006 53.3E5004

0.13 20.2/41 51.2/046E5006 1.1=664E5006 53.?E5004

0.14 20.2/41 51.243=6E5006 1.2164=E5006 53.1E5004

0.1> 20.2/41 51./?2=2E5006 1.23=36E5006 56.3E5004

0.2 20.2/41 51./>=3/E5006 1./////E5006 56.2E5004

0.21 20.2/41 51.??320E5006 1./4>=/E5006 5=.4E5004

0.22 20.2/41 51.?>6>2E5006 1.???/E5006 5=./E5004

0.2/ 20.2/41 51.=??>0E5006 1.?>3=>E5006 5?.3E5004

0.2? 20.2/41 51.=>11/E5006 1.=?>/=E5006 5?.2E5004

0.2= 20.2/41 51.6/=62E5006 1.=>>=?E5006 5/.6E5004

0.26 20.2/41 51.634/3E5006 1.6?412E5006 5/.0E5004

0.23 20.2/41 51.31>/3E5006 0.0000016>= 52.?E5004

0.24 20.2/41 51.3=462E5006 1.3?02=E5006 51.4E5004

0.2> 20.2/41 51.3>61/E5006 1.34/3/E5006 51.2E5004

0./ 20.2/41 51.4/1>0E5006 1.42=?/E5006 56.=E500>

0./1 20.2/41 51.46=>2E5006 1.46=/2E5006 5=.>E5010

0./2 20.2/41 51.4>41>E5006 1.>0//3E5006 =.14E500>

0.// 20.2/41 51.>243/E5006 1.>/>==E5006 1.04E5004

0./? 20.2/41 51.>=3=1E5006 1.>3/42E5006 1.6/E5004

0./= 20.2/41 51.>4?==E5006 2.0061=E5006 2.16E5004

0./6 20.2/41 52.00>4=E5006 2.0/6=2E5006 2.63E5004

0./3 20.2/41 52.0//?1E5006 2.06?>1E5006 /.1=E5004

0./4 20.2/41 52.0==21E5006 2.0>12>E5006 /.61E5004

0./> 20.2/41 52.03=24E5006 2.11=6?E5006 ?.0?E5004

0.? 20.2/41 52.0>/60E5006 2.1/3>/E5006 ?.?/E5004

0.?1 20.2/41 52.11013E5006 2.1=416E5006 ?.40E5004

0.?2 20.2/41 50.00000212= 2.136/E5006 =.1/E5004

0.?/ 20.2/41 52.1/404E5006 2.1>2/?E5006 =.?/E5004

0 0.1 0.2 0./ 0.? 0.= 0.6 0.3 0.

50.000002=

50.000002

50.000001=

50.000001

50.000000=

0

0.000000=

0.000001

0.000001=

0.000002

0.000002=

e6ections

"S &elta (pplied 9oad &elta Sum &eltas


7/19

0.?? 20.2/41 52.1?>?/E5006 2.20623E5006 =.64E5004

0.?= 20.2/41 50.0000021=> 2.21404E5006 =.>1E5004

0.?6 20.2/41 52.16643E5006 2.2233=E5006 6.0>E5004

0.?3 20.2/41 50.00000213/ 2.2/=24E5006 6.2/E5004

0.?4 20.2/41 52.133/?E5006 2.2?066E5006 6.//E5004

0.?> 20.2/41 50.00000214 2.2?/4>E5006 6./>E5004

0.= 20.2/41 52.1404/E5006 0.0000022?= 6.?1E50040.=1 20.2/41 50.00000214 2.2?/4>E5006 6./>E5004

0.=2 20.2/41 52.133/?E5006 2.2?066E5006 6.//E5004

0.=/ 20.2/41 50.00000213/ 2.2/=24E5006 6.2/E5004

0.=? 20.2/41 52.16643E5006 2.2233=E5006 6.0>E5004

0.== 20.2/41 50.0000021=> 2.21404E5006 =.>1E5004

0.=6 20.2/41 52.1?>?/E5006 2.20623E5006 =.64E5004

0.=3 20.2/41 52.1/404E5006 2.1>2/?E5006 =.?/E5004

0.=4 20.2/41 50.00000212= 2.136/E5006 =.1/E5004

0.=> 20.2/41 52.11013E5006 2.1=416E5006 ?.40E5004

0.6 20.2/41 52.0>/60E5006 2.1/3>/E5006 ?.?/E50040.61 20.2/41 52.03=24E5006 2.11=6?E5006 ?.0?E5004

0.62 20.2/41 52.0==21E5006 2.0>12>E5006 /.61E5004

0.6/ 20.2/41 52.0//?1E5006 2.06?>1E5006 /.1=E5004

0.6? 20.2/41 52.00>4=E5006 2.0/6=2E5006 2.63E5004

0.6= 20.2/41 51.>4?==E5006 2.0061=E5006 2.16E5004

0.66 20.2/41 51.>=3=1E5006 1.>3/42E5006 1.6/E5004

0.63 20.2/41 51.>243/E5006 1.>/>==E5006 1.04E5004

0.64 20.2/41 51.4>41>E5006 1.>0//3E5006 =.14E500>

0.6> 20.2/41 51.46=>2E5006 1.46=/2E5006 5=.>E5010

0.3 20.2/41 51.4/1>0E5006 1.42=?/E5006 56.=E500>

0.31 20.2/41 51.3>61/E5006 1.34/3/E5006 51.2E5004

0.32 20.2/41 51.3=462E5006 1.3?02=E5006 51.4E5004

0.3/ 20.2/41 51.31>/3E5006 0.0000016>= 52.?E5004

0.3? 20.2/41 51.634/3E5006 1.6?412E5006 5/.0E5004

0.3= 20.2/41 51.6/=62E5006 1.=>>=?E5006 5/.6E5004

0.36 20.2/41 51.=>11/E5006 1.=?>/=E5006 5?.2E5004

0.33 20.2/41 51.=??>0E5006 1.?>3=>E5006 5?.3E5004

0.34 20.2/41 51.?>6>2E5006 1.???/E5006 5=./E5004

0.3> 20.2/41 51.??320E5006 1./4>=/E5006 5=.4E5004

0.4 20.2/41 51./>=3/E5006 1./////E5006 56.2E5004

0.41 20.2/41 51./?2=2E5006 1.23=36E5006 56.3E5004

0.42 20.2/41 51.243=6E5006 1.2164=E5006 53.1E5004

0.4/ 20.2/41 51.2/046E5006 1.1=664E5006 53.?E5004

0.4? 20.2/41 51.132?1E5006 1.0>=24E5006 53.3E5004

0.4= 20.2/41 51.11222E5006 1.0/23/E5006 53.>E5004

0.46 20.2/41 51.0=02>E5006 >.6>042E5003 54.1E5004

0.43 20.2/41 5>.46603E5003 >.0?/>?E5003 54.2E5004

0.44 20.2/41 5>.21142E5003 4./43/1E5003 54.2E5004


8/19

0.4> 20.2/41 50.0000004=? 3.321=4E5003 54.2E5004

0.> 20.2/41 53.4=0>>E5003 3.0?3?1E5003 54.0E5004

0.>1 20.2/41 53.1???0E5003 6./6=?>E5003 53.4E5004

0.>2 20.2/41 50.0000006?2 =.636=1E5003 53.?E5004

0.>/ 20.2/41 5=.63444E5003 ?.>4114E5003 53.0E5004

0.>? 20.2/41 50.000000?>2 0.000000?24 56.?E5004

0.>= 20.2/41 5?.1?/=4E5003 /.=3???E5003 5=.3E50040.>6 20.2/41 50.000000//= 2.46?==E5003 5?.>E5004

0.>3 20.2/41 52.=/4?>E5003 2.1=1/=E5003 5/.>E5004

0.>4 20.2/41 50.000000131 1.?/=6?E5003 52.3E5004

0.>> 20.2/41 54.6/604E5004 3.142?4E5004 51.=E5004

1 20.2/41 0 0 0


9/19

suares

0

2.112>3E5016

3.=1?=/E5016

1.?>43/E501= denom

2./=?21E501= >.442/=244/1

/.2/>12E501=?.0>224E501= 1.2/=2>?110?

?.46346E501=

=.=//21E501=

6.066>3E501=

6.?=323E501=

6.30014E501=

6.3>421E501=

6.3=>0?E501=

6.=>?/3E501=

6./1446E501==.>?>20E501=

=.=0//6E501=

?.>>>44E501=

?.?=32=E501=

/.4>/?/E501=

/./2=??E501=

2.364>>E501=

2.2/426E501=

1.3?=64E501=

1./0136E501=

>.1=064E5016

=.>21?4E5016

/./3=?6E5016

1.=/4=6E5016

?.140/1E5013

/.=1/10E501>

2.64?22E5013

1.131?>E5016

2.6=4=0E5016

?.66?1?E5016

3.11/>1E5016

>.>2616E5016

1./01?1E501=

1.62433E501=

1.>6==>E501=

2./0242E501=

2.6/16>E501=

2.>?/4/E501=

0.> 1


10/19

/.2/1?6E501=

/.?43=6E501=

/.30=>/E501=

/.441/6E501=

?.00>30E501=

?.043>2E501=

?.11?20E501=?.043>2E501=

?.00>30E501=

/.441/6E501=

/.30=>/E501=

/.?43=6E501=

/.2/1?6E501=

2.>?/4/E501=

2.6/16>E501=

2./0242E501=

1.>6==>E501=1.62433E501=

1./01?1E501=

>.>2616E5016

3.11/>1E5016

?.66?1?E5016

2.6=4=0E5016

1.131?>E5016

2.64?22E5013

/.=1/10E501>

?.140/1E5013

1.=/4=6E5016

/./3=?6E5016

=.>21?4E5016

>.1=064E5016

1./0136E501=

1.3?=64E501=

2.2/426E501=

2.364>>E501=

/./2=??E501=

/.4>/?/E501=

?.?=32=E501=

?.>>>44E501=

=.=0//6E501=

=.>?>20E501=

6./1446E501=

6.=>?/3E501=

6.3=>0?E501=

6.3>421E501=


11/19

6.30014E501=

6.?=323E501=

6.066>3E501=

=.=//21E501=

?.46346E501=

?.0>224E501=

/.2/>12E501=2./=?21E501=

1.?>43/E501=

3.=1?=/E5016

2.112>3E5016

0


12/19

Microsoft Excel 15.0 Answer Report

Worksheet: [Mander.xlsx]Sheet#

Report reated: !"10"#015 10:78:#5 AM

Res%lt: Sol&er has con&er*ed to the c%rrent sol%tion. All onstraints are sati

Sol&er En*ine

Engine: E$olutionar

Solution Time: 0.12= Seconds.Iterations: 0 Subproblems: 2

Sol&er +ptions

Max Time nlimited! Iterations nlimited! "recision 0.000001! se (utomatic Scalin

#on$ergence 0.0001! "opulation Si%e 100! Random Seed 0! Mutation Rate 0.03=! Ti

Max Subproblems nlimited! Max Integer Sols nlimited! Integer Tolerance 1'! (ss

)b*ecti$e #ell +Min,

ell ,a'e +ri*inal -al%e inal -al%e

-7-> sum suares ?.1106>32E501/ 1.2=4=?E5012

ariable #ells

ell ,a'e +ri*inal -al%e inal -al%e /nte*er

-7-? alpa 0.1 0.2646004206 #ontin

-7-= #1 1 0.?==464>>23 #ontin

#onstraints

ell ,a'e ell -al%e or'%la Stat%s Slack

-7-? alpa 0.2646004206 -7-?;0.? Not 7inding 0.1/1/>>13>?-7-? alpa 0.2646004206 -7-?>23 -7-=;0.== Not 7inding 0.0>?1/1003/

-7-= #1 0.?==464>>23 -7-=>23


13/19

s)ed.

g

me @Fo Impro$e /0 sec! Reuire 7ounds

me NonNegati$e


14/19

@d 4 x del"S del(pplied Sum suare su

9 = 0 0 0 0 0

" 16 0.01 50.000000031 3.14E5004 4./6E5010 6.>>E501>

alpa 0.2> 0.02 51.?1>04E5003 1.??E5003 1.66E500> 2.3?E5014

#1 0.? 0.0/ 52.126>0E5003 2.1=E5003 2.?=E500> =.>4E5014

E 2>000 0.0? 52.4/26?E5003 2.46E5003 /.1>E500> 1.02E5013

I 1000 0.0= 5/.=/=6/E5003 /.=3E5003 /.44E500> 1.=1E50130.06 5?.2/=13E5003 ?.24E5003 ?.=1E500> 2.0/E5013

sum suares 1.=046E501? 0.03 5?.>/0=3E5003 ?.>4E5003 =.06E500> 2.=6E5013

0.04 5=.6211=E5003 =.64E5003 =.=?E500> /.06E5013

0.0> 56./0621E5003 6./3E5003 =.>/E500> /.=1E5013

0.1 56.>4=06E5003 3.0=E5003 6.2?E500> /.4>E5013

0.11 53.6=301E5003 3.32E5003 6.?6E500> ?.13E5013

0.12 54./21/4E5003 4./>E5003 6.=>E500> ?./=E5013

0.1/ 54.>33?3E5003 >.0?E5003 6.6=E500> ?.?2E5013

0.1? 5>.62?60E5003 >.6>E5003 6.62E500> ?./4E5013

0.1= 51.02621E5006 1.0/E5006 6.=2E500> ?.26E50130.16 51.044>2E5006 1.10E5006 6./6E500> ?.0=E5013

0.13 51.1=0=/E5006 1.16E5006 6.1=E500> /.34E5013

0.14 50.000001211 1.22E5006 =.4>E500> /.?6E5013

0.1> 51.23016E5006 1.24E5006 =.=>E500> /.1/E5013

0.2 50.000001/24 1.//E5006 =.2>E500> 2.40E5013

0.21 51./4?==E5006 1./>E5006 ?.>4E500> 2.?4E5013

0.22 51.?/>61E5006 1.??E5006 ?.6>E500> 2.20E5013

0.2/ 51.?>/1=E5006 1.=0E5006 ?.??E500> 1.>3E5013

0.2? 51.=?=10E5006 1.==E5006 ?.2=E500> 1.40E5013

0.2= 51.=>=?0E5006 1.60E5006 ?.1?E500> 1.31E5013

0.26 50.0000016?? 1.6=E5006 ?.1?E500> 1.31E5013

0.23 51.6>036E5006 1.30E5006 ?.23E500> 1.4/E5013

0.24 51.3/=64E5006 1.3?E5006 ?.=3E500> 2.0>E5013

0.2> 51.33463E5006 1.34E5006 =.06E500> 2.=6E5013

0./ 51.41>63E5006 1.4/E5006 =.36E500> /./2E5013

0./1 51.4=463E5006 1.43E5006 6.66E500> ?.?/E5013

0./2 51.4>=63E5006 1.>0E5006 3.31E500> =.>?E5013

0.// 51.>/063E5006 1.>?E5006 4.44E500> 3.4>E5013

0./? 51.>6/63E5006 1.>3E5006 1.02E5004 1.0/E5016

0./= 51.>>?63E5006 2.01E5006 1.1=E5004 1./2E5016

0./6 52.02/63E5006 2.0?E5006 1.2>E5004 1.6=E5016

0./3 52.0=063E5006 2.06E5006 1.?2E5004 2.0/E5016

0./4 52.03=63E5006 2.0>E5006 1.=6E5004 2.??E5016

0./> 52.0>463E5006 2.12E5006 1.30E5004 2.44E5016

0.? 52.11>63E5006 2.1?E5006 1.4/E5004 /./?E5016

0.?1 52.1/463E5006 2.16E5006 1.>=E5004 /.40E5016

0.?2 52.1==63E5006 2.14E5006 2.06E5004 ?.26E5016

0.?/ 52.13063E5006 2.1>E5006 2.13E5004 ?.30E5016

0 0.1 0.2 0./ 0.? 0.= 0.6 0.3 0.4 0.> 1

50.000002=

50.000002

50.000001=

50.000001

50.000000=

0

0.000000=0.000001

0.000001=

0.000002

0.000002=

&eDections

"restress &elta (pplied &elta Sum


15/19

0.?? 52.14/63E5006 2.21E5006 2.26E5004 =.11E5016

0.?= 52.1>?63E5006 2.22E5006 2./?E5004 =.?4E5016

0.?6 52.20/63E5006 2.2/E5006 2.?1E5004 =.40E5016

0.?3 52.21063E5006 2.2?E5006 2.?6E5004 6.06E5016

0.?4 52.21=63E5006 2.2?E5006 2.=0E5004 6.2=E5016

0.?> 52.21463E5006 2.2?E5006 2.=2E5004 6./6E5016

0.= 52.21>63E5006 2.2?E5006 2.=/E5004 6.?0E50160.=1 52.21463E5006 2.2?E5006 2.=2E5004 6./6E5016

0.=2 52.21=63E5006 2.2?E5006 2.=0E5004 6.2=E5016

0.=/ 52.21063E5006 2.2?E5006 2.?6E5004 6.06E5016

0.=? 52.20/63E5006 2.2/E5006 2.?1E5004 =.40E5016

0.== 52.1>?63E5006 2.22E5006 2./?E5004 =.?4E5016

0.=6 52.14/63E5006 2.21E5006 2.26E5004 =.11E5016

0.=3 52.13063E5006 2.1>E5006 2.13E5004 ?.30E5016

0.=4 52.1==63E5006 2.14E5006 2.06E5004 ?.26E5016

0.=> 52.1/463E5006 2.16E5006 1.>=E5004 /.40E5016

0.6 52.11>63E5006 2.1?E5006 1.4/E5004 /./?E50160.61 52.0>463E5006 2.12E5006 1.30E5004 2.44E5016

0.62 52.03=63E5006 2.0>E5006 1.=6E5004 2.??E5016

0.6/ 52.0=063E5006 2.06E5006 1.?2E5004 2.0/E5016

0.6? 52.02/63E5006 2.0?E5006 1.2>E5004 1.6=E5016

0.6= 51.>>?63E5006 2.01E5006 1.1=E5004 1./2E5016

0.66 51.>6/63E5006 1.>3E5006 1.02E5004 1.0/E5016

0.63 51.>/063E5006 1.>?E5006 4.44E500> 3.4>E5013

0.64 51.4>=63E5006 1.>0E5006 3.31E500> =.>?E5013

0.6> 51.4=463E5006 1.43E5006 6.66E500> ?.?/E5013

0.3 51.41>63E5006 1.4/E5006 =.36E500> /./2E5013

0.31 51.33463E5006 1.34E5006 =.06E500> 2.=6E5013

0.32 51.3/=64E5006 1.3?E5006 ?.=3E500> 2.0>E5013

0.3/ 51.6>036E5006 1.30E5006 ?.23E500> 1.4/E5013

0.3? 50.0000016?? 1.6=E5006 ?.1?E500> 1.31E5013

0.3= 51.=>=?0E5006 1.60E5006 ?.1?E500> 1.31E5013

0.36 51.=?=10E5006 1.==E5006 ?.2=E500> 1.40E5013

0.33 51.?>/1=E5006 1.=0E5006 ?.??E500> 1.>3E5013

0.34 51.?/>61E5006 1.??E5006 ?.6>E500> 2.20E5013

0.3> 51./4?==E5006 1./>E5006 ?.>4E500> 2.?4E5013

0.4 50.000001/24 1.//E5006 =.2>E500> 2.40E5013

0.41 51.23016E5006 1.24E5006 =.=>E500> /.1/E5013

0.42 50.000001211 1.22E5006 =.4>E500> /.?6E5013

0.4/ 51.1=0=/E5006 1.16E5006 6.1=E500> /.34E5013

0.4? 51.044>2E5006 1.10E5006 6./6E500> ?.0=E5013

0.4= 51.02621E5006 1.0/E5006 6.=2E500> ?.26E5013

0.46 5>.62?60E5003 >.6>E5003 6.62E500> ?./4E5013

0.43 54.>33?3E5003 >.0?E5003 6.6=E500> ?.?2E5013

0.44 54./21/4E5003 4./>E5003 6.=>E500> ?./=E5013


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0.4> 53.6=301E5003 3.32E5003 6.?6E500> ?.13E5013

0.> 56.>4=06E5003 3.0=E5003 6.2?E500> /.4>E5013

0.>1 56./0621E5003 6./3E5003 =.>/E500> /.=1E5013

0.>2 5=.6211=E5003 =.64E5003 =.=?E500> /.06E5013

0.>/ 5?.>/0=3E5003 ?.>4E5003 =.06E500> 2.=6E5013

0.>? 5?.2/=13E5003 ?.24E5003 ?.=1E500> 2.0/E5013

0.>= 5/.=/=6/E5003 /.=3E5003 /.44E500> 1.=1E50130.>6 52.4/26?E5003 2.46E5003 /.1>E500> 1.02E5013

0.>3 52.126>0E5003 2.1=E5003 2.?=E500> =.>4E5014

0.>4 51.?1>04E5003 1.??E5003 1.66E500> 2.3?E5014

0.>> 50.000000031 3.14E5004 4./6E5010 6.>>E501>

1 0 0 0 0


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