ISYE 6414 Midterm Exam Part Solutions| With complete solution| Updated RATED A+ | NEW EDITION| Georgia Institute Of Technology

01234565789 3  18



!"#
!$$% %$%
% &'&'
()*+,-.+/0)*
123456789:;<=>?@3=A?B:@4C2@DB@4C3;=4EC2@@FGCHA;:@A2B=94@AC3;=4I;8H;B8A;:@E7=:C2@C@JC
K?;A94I;8H;B88@4G;=4@4LM=4<@8C2@DB@4C3;=4K@?;<KHA;FG?@C3=NC2@56789:;<=>?@LO;BFB4C
7=4<@8C2@DB@4C3;=4B43=NC234>?@LO;BA7=A27=N@C2@I;8F7CI8;F G:IC;P;8:;82CF?7=:F79@
;C2@84?3N2C7:QB4CF@=C4C;N@CC2@>?@C;9=3CKBC;C2@8<34@9@@GC2@I;8F7CC3=NC2@47F@LR=A@H;BST@
>=342@:7=4<@83=NC2@DB@4C3;=4E4BKF3CH;B88@4G;=4@43=743=N?@9=3CC@:>?@UQB4C?39@C2@2;F@<;89G@@8
744@44F@=C4VL
12@8@78@WXDB@4C3;=4C;C7?E@7A2<;8C2K@C<@@=YZ[G;3=C4L\78C37?A8@:3CF7HK@N3T@=3IH;B8A;:@34
A;88@ACKBCH;B8A;=A?B43;=343=A;88@AC;8T3A@T@847L
]^_`a`^bcd
WLe7T@C234fghi>?@3=H;B8g<;893=N:38@AC;8HZC2@47F@:38@AC;8H<2@8@H;B<3??:;<=?;7:C2@
jklmnokpqfplr:7C7>?@3=C;Ls7T3=NK;C2>?@43=C2@47F@:38@AC;8H<3??2@?G3=8@7:3=NC2@fplr
>?@L
YL5@7:C2@DB@4C3;=7=:A8@7C@C2@5A;:@=@A@4478H<3C23=C2@A;:@A2B=94@AC3;=3FF@:37C@?HK@?;<
@7A2DB@4C3;=Lt=3CC3=NC234>?@<3??N@=@87C@C2@;BCGBC7=:3=4@8C3C3=C;C2@4@AC3;=K@?;<C2@A;:@
A2B=9L
uL1HG@H;B87=4<@8C;C2@DB@4C3;=43=C2@C@JCK?;A9G8;T3:@:3FF@:37C@?H7IC@8C2@8@4G;=4@G8;FGCv
wxyzyzx{| }x~~z€{z~€{‚€}|yƒƒ„~ {‚†}}~‡L
[LR=A@H;BST@>=342@:7=4<@83=N7??DB@4C3;=4E9=3CC234>?@7=:4BKF3CC2@9=3CC@:>?@;=ˆ7=T74L
‰_Š‹bŒ^Ž^c`‘’“‹Š`d
UW7V1234<3??K@C2@@J7FDB@4C3;=Z@7A2DB@4C3;=347?8@7:HA;G3@:I8;Fˆ7=T747=:3=4@8C@:3=C;3=:3T3:B7?
C@JCK?;A94K@?;<E”Ž•‘`‘^^•`–b”—bŠc`^`˜^™Ž^c`‘cš“‹`˜^‘Œ‘^›Š‘œŠc^_Š‹
žŸ¡¢£¤¥¦§¨¥¦©ª«¬¡­¥¡®Ÿ«¯¥­°§ª­¦§¨¥±¥¤§²¯©¥¦§¢¢¥«¯³
´~z€{z~}{µ¶~z}y{·¸†¹v123434C2@4@AC3;=<2@8@H;BCHG@H;B8<83CC@=7=4<@84C;C2@DB@4C3;=L
º@G@=:3=N;=C2@DB@4C3;=749@:EH;B8CHG@:8@4G;=4@F7HK@7=BFK@8E7?34C;IT7837K?@4E7I@<4@=C@=A@4E
;87A;FK3=7C3;=;IC2@4@@?@F@=C4L
´~†‡»¼½~}¾z„~¿yÀ



W

, 0121342516789






!
"
"




"#
$%&'()*&+,-+'./

"0


 1!!
#2"33


!40

5
6#*7,5!3/
8"
9#',:5"""!3


;#<=%5>/0!  !3

!
0
!



0!
?"03

!@A!BC9D!3
@ A!D
E3!@ C9D

6F#G9H#I
H#+J%KL),&5M
3"
 "0

"BM
3/
G#'=NO,)5A@ D
P#),7%N&5
8"Q
 RS 
 
#
4#+J*)7,'520
"
"




"
T41 0121
U
E


#VWXYZX[\]Z\^_`a^W`bcdbefgfh3/#
ijklmnokmlnlpkn
=qL*r*stuvwxyz{|}%&'()*&+,-+'.}~J,*L,)s€‚~'r)%&7'ƒ'„*+rN)'s€‚
i†kn‡kˆl‰kŠ‹ŒŠlm†ŒŽnoklpnlpnoklpk‰k‘Žl‰nln’k’l‰Žkp
=qL*r*s“”•–”—|=qL*r*~',:˜™tušu{uš|',:~),›s}›,=*K,}
=qL*r*s“”•–”—|=qL*r*~'=NO,)˜™tušu{uš|'=NO,)~),›s}&N}
=qL*r*s“”•–”—|=qL*r*~),7%N&˜™tušu{uš|),7%N&~),›s}'N(rJ,*'r}
œ 42ž Ÿ ¡¢£¤9129¥¦ 1¤¥ž1 ¦§¨©¦
@6D9/ª«ª
ª
/
"/!/0

+J*)7,'"3),7%N&
"!#> 
/
),7%N&//3
 /"!+J*)7,'¬2"
!#
i­ŒmknŒ®¯klnkŒ°±‰Œn²²²
³´µ¶š´•|+J*)7,'·),7%N&~L*r*s=qL*r*~qK*<s¸¹J*)7,'¸~:K*<s¸€,7%N&¸~
=*%&s¸ºN:»KNrN›¹J*)7,'.'-€,7%N&¸~+NKs¸7)*q¸~»+Js¼½




9