Solutions manual for operations research an introduction 10th edition by taha ibsn 9780134444017

SOLUTIONS MANUAL for Operations Research An Introduction 10th
Edition by Taha IBSN 9780134444017
Full download: http://downloadlink.org/p/solutions-manual-for-operations-
research-an-introduction-10th-edition-by-taha-ibsn-9780134444017/
CHAPTER2
Modeling with Linear Programming
2-1
.•

l
«'x, x. >- 0 j+
Chapter 2
(a.) Xz. - x, >- I _,,, - )('1
-r X.._ � I I I
ChJ x, -i-:lx.._ � 3 a� x,-t:Jx, �,
(<;} X2. � X1 Or x1 - Kz. � 6
(d) x, -i- x. ?:- 3
ce>
o» ,x., .'1) = (t, 'i)
(,c, ,x,) ;.. o
,x/+41('1 =�:Z
I ;c I + :1../l 'I = 'J
(bJ o; .x.J -=- ( z., z.J
(
,x
x., ,J.) � 0
sx,+�l(.J o$X1�?..
z-
"/,!,)(1 -r 4Xz > x, » :l.
Z -f 4)(1-
I xz.
'= .20
= -=c Zt
<:
/1 (e1s,Mt.
+ :z.J<.2. 6
-1 J(l + I XZ = 0
I XZ. :Z.
< I
= :z
Z= sx2+1x2. .. $18
(CJ (J(',, ,c,.) :: ( S, I·�)
)(, >)(�?: 0
6x3-r'IXl·S"'= �L/
I lt.3 + .2.)1. ss: ::: 6
-llt3 +I xt� :-l·S
I X t-s : J. S°
Z = 3"x3+ �x,.,; =
(.IJ (!, -> x.) = (:t, I)
z. 'IX I = I 6, <.:t -'f fus,·1.f.,_
< '/ JC 2 + ZXI "' ,q
-JICZ. +/XI : •I < I
/,Cl ,,i < 2.
Z::. Sxl -t 4JCI = st«
(.e) (x,, x,) = (.1, -I) .
)(
1
� 0 J x; < 0 I .;,..�
�, (c) 1i:-i1,. 4£ {� �
cx.,X2. > -= < z, .2) 1 3,k(;" S
1
a,,,./ .s._ l,e fk u-.,...,.,._,(� �
�..c;'f!_ HI� 1-13..
ro, Ml: :s, = .t'I- c,x;-t '(Xi.)= 41,n.r/d""/
!b,,fo'll1 s:i:: ,-f, -,.�,.... )
= ,_ (.t -r.2XZ) .::. 0 fonr /t/o.At
2-2

>
·$ (c) -x,t-x, = I
_J?;�(!)-1<---:,,�x,
Chapter 2
°(
",
�, z
..l = fi/3
IQ)
-4
(C) x.,
(e)
(b)
8
M��e, Z = �i<, + 3Xi.
s. t .
(Cl
(a) x,��-s
Xz:� .<J
(h) x. ;,: z.
oplrm•in,
c.t-S", 1·1S)
i-: '$1'1·50
oplrm,im:
( -2, 2.)
-'l, .. f/{f
+
/O'J<, +- s Xz. .:1: eoo (I)
6X, +-.ioXz._ S..600 (2.)
Kx,+JoX._ �&oo (3)
0� O"CCu-t.c o,I- r/:
x., '= 5�-99
X2. :- 19-12
"7''-t--'�.._.. ;"t-....::::.....,_�_X,
continued...
2-3
2 -= :!J. Ir.ff. :J'{
. .- .

Chapter 2
;<, = nu,,..H-, cl} � .!/ A
><z=�1�fB
x, = .t .,,.;.,uwu1 ..,;, A
I I
K,. = ¢ � -· B
Ma::x� Z = :l.o ;;<1 T 5 o)('._
Mt1,<lmi2e Z = · OSX1 + · 01'><2-
-..:x...:,..-�-8
X1+Xi.
x, � Joo
�x, + q.x,. � .fl. q.,o
x,, JC._ �o
So
s.r.
5"100
X, � .:2s (x,"fX'a)
)(._ � · S ( X1+ X.)
I( I <l' • $" )(l.
)( -t X;i. .5: So1101
x., �'&, � 0
�-:
>C, -:.
4:tS-00
x._:,:isoo
z.:. t 3:lS"'
, I
oph·rnwm.'
><;"'" �a
)(._,.10
Z -�"'"' Ooo
a
q,.,Jr- J"•.&,.:J,-p,.:
X, = "SSO slieek
Xz "(S1.t3 1,,,1"1
Z =- f.,.t. 'lf,S"f'/. '( o
<Foo
2-4

-...c;-1�
+
.,-.."'tAf-
x, ... �tl �19
x.. = 1s
m.r::I'� }- "' £> K,-,. 10 xl..
�Grc;- .
•S-X, -r • S- XL :!:.. I SO
., XI -f • 'fX L � /'-fS-
X., e 3 o
X1 � IS?J
Xz.
Chapter 2
13
1£...L...L..�..::::__...:::::....::=.t-��....::::.""<::�1
100 300
qph·mw.., : X," �oo, X,a. "' So , z =$l. ,1,S'o
/J,u alltJCUbn: ,1, 7rano, .ss%wJ,a,.h�
.x,,
x.._
.)(.I.>-. 0 i:, .. r'� �-,-..a1"::I )5x.. : ,,.,,;...,.. �
,,,,,,II >t:w,1.,te i! : .:l. x, + X 2..
$,/;. X X �(OI L
X1 - Xa. 1' 0
;<, � '(
ic; , x, !>- 0
Oplrn1•m .r,r/,,,{;,,.:
• JiI : -'/ k,,.,s
h= '-1.nws
z. e I I./ "ffunrifs"
x,
x, =� ...i,,.. f�' l'u.r
Xz. ,,_ 'DoihJ ?1br. 'b "8-r-� !o./•
/ollp.x.1ir11'z e z» llX, «sXz.
s.r- .tx; -t X2. 5 9-dO
x, � /s»
Xz. s ::/. aa
.•,
x ::: ns« of � 4,rxao
x: = nbr. 61 uheo:tl l,,,xc,o
fVJi�1m,zc z = x, .,. , .3,;; x.,_
.s;«, ·2.X,-t·ll-Xz. S�o
x, ::!, 2. 00
Xz. � I2. o
x,,ti � o
.14 oellmum:
;(,= Joo 'jr& I
.<.. ::. :u, 'ir"" 'Z
Z: $/800

continued ... continued...
2-5

1
O:
Ohapterz
x1 = ll.a..4A.o �
X,..= TV�
/Vt al<t'm i ze, z = x, -,. �sXz..
Op/;{mum Oc:<:UrJ" a..-I- fl:
x, = s- ,� K tr,,.,$ f'6t' ftn,,.,.
x.. s 10•.2.S"&. �,,.. � -hw,..._
z • /S3, F�6 lb rf Sfu.rn
s,». IS'l< +-.3oaxz. ,s 10,,ao
OplrmlA / r,•J,'i, = :I.:.!1:..t' = . !,-
-x,
x:..
�.....z or -><, -t Z.J(� � o 10· >SI.
(l,J � ./ x, + · 9 Xi. �(� o+ 1) ::..Z t
IOd
)(I � �ooj 1(1, l(� '?'O
5)C, .. .3oo)(z :IOIOO
.?
CJ;>!,·,.,,.,.., Z = 1,/S38 ",fsl-uw,
6Z = /(,/S38-IS38�i = 7t92. lb
X,:Nbr.af�� 19
b�� fr.r/;
Xz. a Afhr-17V �s brJtml/ ti.. t1rs/;
/Vlox,miz.e. Z: ,1.flOO'lf,-f.3DOll/(z.+S101f 2.0,0
s.e. 300(><,+1) -1-:J.o,oe<i-tO � 2.01000
3 oo CX,+1) � . i,c 2.o, oao
.2.oao cx.+r) � ./?xz.�o•o
�=��'l-_,;;_::::,,..._===--....i....::)r1
Soo 1000
x,.,, ,o.,, .....�
O'l.-
x, > /('. � 0
O'f'� (1U.W..0 """ ,q :
x� = 30.:3 �
z = F/l./8
,c, =-h,ns af C, cart...-.ult--
x., ... fon.r if c2 � � R,_
�lmi te 2' = 1.2000)(1 + 9000 Xi.
,S'.1;.
,Nei)(,'rniz.c. z.-=- �ooox,-t3Pt1ox2-,. 7ouo
s-t-, 3oox+2<HIOX2- � l77oo CD
ae <.. IS7oo ©"I -
.:lOOOKz. !: 11{-0()0 @)
18 )(,, x; �"
/EooX1
-I ;(loo)(,_::!: !loao(X,+X�)
- .:J 00 X, + /00 X._ � 0
.2.J x., + . 1 x, � 2.o
X,>)(,_�O
Xi.
aa
IO
continued ...
2-6

Op./:,mum �';/,,... :
l<o,l.,o C-.,rotKc•.lr: e �:l.·J3-t-l
= '53. !13
rir ,.,l.r = I -f"I = :l

a"'
=
�I
1
x,-::.�1�,_.�
x..... �;;;�,r�
,,v1 ,;c,,.;.,iz.e. z = 'lx, r 1J.�,.
Chapter 2
20 X,= � 'J- f/;Ft1 �
. Jlz. = � 1ff,"F,·z. �
O�,
se.
:,.0x,+6o x,." :tsx6o = /soo
1ox, +6oxt. � 3S"X6o := :1..100
(I)
(Z)
'� + "I-Xz.
e x, + ex;
.,.,_.
4X1 + 6X,._
1i. 4FOx·'I = 43Z.
�-4RaX·E6: 4IZ·8
!!::. if-Rox. 8'1 = 'IZZ-i./
;�x, + 4Xi � 5i<6o • 3oa
)( I> J("L � C:,
(!J
6X + 4")(.._ -f s1
:43Z
oph"mo,., o.t II:
X,: a sRtrfs/1,,..
X1,:: ./fl /,/111s04/l!J..
z. ... :f. r/I?>...
A
5"X1 «s x; «s; :4/Z-8
4x1 +6 X2.. + s3 = L/Zl.�
Clbicdtile. /�en..
M,n,mizc s; -,._s; +S3 =IZ{,7.2-ISX,-ISX,.
7A,u,, m'>1 S,+Sz.+.S, m11,r 1sx, +1sx._
/Jll�;x,miie Z: /s:»; r/S")(z..
)(I = pbr. df duK.r f'4' """'I-
X,_ = tJbr. 4 ch.airs !"" d41f
$ ./-•
6X, "/-� X,._
:ic,._ 5)<, + s:){l.
4X, + ')( �
)(_,,XL �c:)
� "'132
�4/Z.5"
�4Zl.�
;11A�m><�e Z = SO X1 + /00 X,_
x, )(,.. ( I)
uii t Ki
( Altunah. .I/<.- "
-'
�t"'
-- exist)
· · �, � so.11r "'�;-Is
l<z :.3/ .{,l1 (.fnjfs
_x, _,. l(,_ ( ?.) ,.,.,...._._ z-.123'8.l/ ,.,,n
rs» uo <.- I
110
ya
(,o
x, � /;). 0, Xi� 60 (3,4)
x....
o..c-L..L.L.L..LJ.'J..J.��. x,
100
ZJ
Comer point
A
B
z
(O.O) 0
(4.0) 20
Opl,"m<Am:

x, ="'JO�
X;i..-. 4'1 Clrfl1fl
z = $ 8'/tJO
c
D
E
F
2-7
(3,1.5)
(2,2)
(1,2)
(O, l)
21 (OPTIMUM)
18
13
4

:.
o 12 1, lo
Chapter 2
(Q)
28 '30
_,. �---'-�
10110 I
�·· ..>e; =«, Xz.. :a., Z=o .J
4dt.:ci' i� nons�.r,'J
(C)
a..,J,/d,.rr,J =+r11.lnI :
ll-..
>', "' � ol'j;,_,,s/111orlt. .,;, sir,,... 1 3 I
x,. • �-j "-/we.cit. .•.,.; &frtre.i.
J1,'nimiz� z,. .?X,-t{Xz.
s.t.
x, + x, � eo
5 � x, � 12.
, '!:- x� � Io
So•
500
�Jdwl,11n,
x, -::::. 45'0 lb X1..
-= ,3£'0 /!,;, z
-= ,4SQ
1000
continued ...
2-8
<I
+--4�-�.�--l----'--�--x,
X1
IO �.s
X2 � /o �s
2 : 1 'I- o sf,rsi index
continued...

2
32 ot.t-
Chapter 2
33
.Al/,r1,mize z: :. x,-,.. X'i.
�4
x; :: 1/# �� u: ck;mt.£
Xa"/0��..;. '°ji-fe<f �
Jiil ,;,,;,,8'" Z: = X, + Xz.
�Ii'
X, � • �(X,1'Xi)
c,t.
_ ., x, +. 1,t x2. � o
• Ix1
-f, :t!:.-X
.(, x, - , ',/ �
::::; Io
:j: 0
·�-'y +• I X'2 � /'/
-�sx, + . t; x2.. ::: 3o
·IX, + ·/S'Xl. ;? IO
,/S'X1 -1-·IXz. �8'
x,., x; �o
X,, Xi ;;,o
LINEAR PROGRAMUIHG- GRAPHICAL SOLUTION
-
LINEAR PROGRAMMING- GAAPHICAL SOWT10N
"'
"'
.. . .............. .
..111
.'"
.
••
71
. ·-
•••

( 6) 0.04
0.03
0.03
( 7) 1.00 1.00
Chapter 2
X, = RJiiofscn.p f) ,,,., al!o.J
34Xi =Rali,(rerr,.pB""' al/'lf
x1 x2
Minimize 100.00 80.00
Subject to
( 1) 0.06 0.03 >= 0.03
( 2) 0.06 0.03 <= 0.06
( 3) 0.03 0.06 >= 0.03
( 4) 0.03 0.06 <= 0.05
( 5) 0.04 >= 0.03
<= 0.07
= 1.00
(Jil
�'6)) 3
x2
Summary of Optimal Solution:
Objective Value = 86.67
x1 = 0.33
x2 = 0.67
<,
( 4)
x1 3

I 4·" - -
'Z 7, 62. +-'· {., Dr:,//; 6omn,Jfm,, 'lft'1
3 4,6Z -,J.O o /Jorror,1/3f-1-1
q o _q,,z I/Jarn,,1/1/.,zf--1-r�
Chapter 2
X,+x,. -+Xy + � :Sl�ooo
·S°l<1+·,Xi -.X3 +·YXif +/.o(,�<f',-.J. :. o
. I 2.
·3X,r·l.X,. +,fX,1+·,xv,+l.06St-� = o
f·'IX,-tl·fXi+l·'l�-+f,lxv+l,o6r� -iv= 0
· I· 'ZJ<, -t/.1Xi +·!X3 +.'J'sXyr l-06'SJI"-� =•
ati�i?o
' TtiRA Clf"twu,J� !
7he �c!J� tffaM.
....,�
X,=o., Xz. e :s/0,000, J<3= f.6000.1 XCf =o
fn-,<.tA.l- """' ..t,.,(i;. � ...... .J-4.1. (#,..
/�/1vcr,jeia:I��
,u,J( 71% c/p17�jecl- 6...; ��.
7l.. fctt-,,..R. � -'-c,u O • t• �
:J If(, 060 -1-o 12. 7, 7:J.O.
I
ff,-:: o, 1-,=o, i, :.'ItKto, <fq. =11s3,' 'tZ.
z = 1s�,er.7 3 o:t ti.. Jf{J,l.,f; '6 'cf""'5
continued...
2-11

Ohapterzi
�ozrs,
lfl+IP,_ l,IP,+l,S1'1. 1,rr,-1.rp2 -l·CP-1,f� ·sP ·2·8f'�
'
1
(a) IY1R')t1'm,'ze. Z = SS"
S.ubjeefti
I, +·'lrC:,1 +1-02.M, = 2,
Iz + ·?f'�L +l·rn.. Mz.
= .:t+l·o7SI1+,o79G1
+•o1sM
l3 +·'IS'C-,3 _ 1
: R·S"+f.a1f'I2 r·011/(61
rG1.)
+ ,o,?S'( /141 +ML)
I4 + . 'II' c,1 .., �-s+ /.07,r� +
·079(6,+G._-+GJ) +
•OBS"( H, + M•)
Ir+ ·'lr<:'t.r= 3 -1-1.07s4 +
·079 (1$, +t;a rG'.s ., Gy) +
·dfS(H, +/lfL)
Ii,= lJ·S+I· o'l.r I-s
+· o7'1Cu, +G• +G.,+G,;,+ Gr)
+ · r.!� (M/tM.J
2-12
continued...

3
Chapter 2
r7 = s.S'-+ /,o1S r, + J;o19 (;1
+·019 (<:,,+ G, + G11 +G,d
r -ess: r1'1, + Md
Ia= 4+ l·o7.s-I7 +1:019<;..,
+ · 079 CG s + Gq + �s)
+· oss (M1 rM,.)
I, =- 4 + /·o7S� -f l·o79 G.1
+ .o» 9 (Gq + Gr)
+ 0
080 (/111 + Htj
..lio = s:«t.ersr1 r l·o7'1 G"
-f·07"f G,r +l·a/J".,H,+ ·OIS/11..
)(LA= -,..-,,..,1-� .... cJ-t'� 144� IJ(looot;) LL!
X,t3=��...·�L:
� /3(1000$)
M"tt?</mizc z « 3 �B + J.7 �'4
suJuce:r to
><,fl + X,B
-/.7 �11 + Xu1 + 18
��o
-·a,1i,1,11 !CllVIIIII � ;.:_
Tiile: 'robt• 2611•14 • ••••·•••··•••··•••·•• ••·•••••04 ••••
,,..1 ltff1tf1111 la1 14
CbJecth• "'..,. c..., • 4'.85ot
"-? X,s -1. 7�
11
"" 0
Vfflmblit V•h• Obj Co.ff DbJ Y•I Contrlb
al 11 ·••••··•••·· D.DOOO··••• D.0000 •••• • • ••••••••••••
al IZ 1,0000 0.0000 D,OOOO
aJ 11 o.0000 o.oooa o.0000
� 14 O,DOOO 0,DOOO 0,0000
a5 IS 0,0000 0.0000 :::::
a6 16 4,6ll1 0,0000 O,OIIOCI
•1 17 9,'1]7 0.0000 0.0000
al II 15,'6711 O,DOOO 0.0000
d i, Z4,666J 0.0000 I 0000
••• 110 37.5201 1.0150 40°.D41
•12 IZ o.oaoo O.DOOO 0.0000
all Gl Z.9051 o.oaoo o
•14 14 l.1]" 0.0000 .:::
alS ID l,9021 1,0790 4,2111
a1' NI 1.960I o.oooa 0.0000
a17 NZ Z,1Z4l 1.11850 Z.3047
C..tr•lnt INS Sl1ck(•l/Surplutl•J ••n••
t <•> z.oooa o.oooa • •••
Z l•J Z.DOOO O,INIOO
l l•I · Z.5000 0.0000
4 <•> Z.5000 0.0000
5 <•> l.DODD O 0000
6 C•J l.5000 0:0000
1 <•> J.5000 o.oooa
I I•) 4.0DDD O.DDDO
' C•J 4.DOOO o 0000
10
Optimum solution: Invest S100,000 in A in yr I and
SI 70,000 in B in yr 2.
Alternative optimum: Invest $100,000 in Bin yr I and
$300,000 in A in yr 3.
X( .. 14,. &UreJj,I� � t, 14.S(•J 5.0000 0:0000
.:.:�Z,�¥
}/=???��
-3>f,+4X, -7X3+1!.Xy
ma:x,mi2c 'Z': .........,,, 5>f1 -3Xz. + '/X3
+ 4Xv
{
sx, - 'iX._ -1-tox -fYy
X1 , x, , X 3 , Xy � o
��cam,fe�.Lr
.. ��<i.o
2-13

1 (>) 0.0000 0.0000+
2 (>) ·0.0000 2262.5000+
3 (>) 0.0000 0.0000+
4 (<) 500.0000 0.0000-
/Jl/ocafi.., f'.J. g7. S-0 --u cJ.q;<-<-- 3
b
7
0
0
(1,-s,,.(/ $ .2. /:2. sO � ck,z,c.eJf. /Z.,_w,i,,v = 8 0
$/175'- CJO q 0
10 0
II 0
/2 0
X a
'·
-3 x; -t 4)(,_ -7 X3 +-IS- X'<f =!- !f•
S I -
3X· i + I� +- 4 X� � y..
3x, - "ix2 + 10 X-.3-.f'xv -::,d•
. x; -t Xi- -t X1 + Xv � s,,o
Xux,_�x3,X'f �"
?!�
- OPTIMUM SOLlfTION SUMMARY -
Title:
Flnal iteration No: 5
Objective value (max) = 1175.0000 .
Variable value Obj Coeff Obj Val Contrib
x1 0.0000 0.0000 0.0000
x2 0.0000 0.0000 0.0000
xJ 287.5000 0.0000 0.0000
x4 212.5000 0.0000 0.0000
x5y 1175.0000 1.0000 1175.0000
Constraint RHS Slacl<(-YSurplus(+)
Chapter 2
,1, = /;/:?,oo, z = - /I.56· 2 '1 'F
��= 0tJO-l/36·l7= &3-1/
Do/!-c,,rr:
t: x:,t; X?,t X31:;
I 0 0 0
2 0 zoo 0
:ir,.qs 313.53 0
3
1 0 537.t/3 0
5 !JJl/.37 z '37.30 0
73'1.6Y 0
sr.:» 0
'l-7 Cf. C,0
89�.IC,
0
2-14·

1
1 2 4
=
3
onn: 0
Ohapterz'
X1,1,::, #NU1'cu,/u-lt! U4v,j/4'1J,,v--h'111<- [47
Xwi = #�/""'- � � ..._.:.....
Xwz = if�/wlc.""tj�
Xe,=# c�/wl. ��u/4 �
Xci =.� c�/w,f. '""""J �
1<cJ =:fl. cf.i,,i,k/ul ""'""'I..tJ.c.,.i.,-w.d.�
M,iJ,'mlz:e. z '-::. :fX +,:.gx11.+3X,, +.f.1x
WI i "'.1 ·i:,
s"�fwto + .1-2.xc.. + �-zXc3
Xj=��i �
p�.w.c,J-j' J-:. ,, -z, 3, 'f
Pl1Jft :F": � '
f'r,.wr,f I= 7S-:J,Xlo-axS-7,:'f = ru.
Prl<MAd �-= 7o -3x10 -zJt s-3x 4 =Ile'
Pr.,aur;/-d = S5-<fJt.lO -l)LS--lX'l=f-2!.
f�� "f = i-S: -2.XfO -21<[.-1,: (f =/I(
Xe., :S S"SO , X1o12 � Z to
.Xc,�,zo, X.,2 s 2 'lo t-1�')1./mize. z « /J.)(,t/9X,:t·2 X3 tit Xl(
x,, + Xca. + J(c3 � 2
Xl>/1 + )(Wl + Xw3
"'1..
s.1;.
.:1)(1 + 3X� Tll-X.3 + 2Xy :!!; SDo
3x + 2x + X3 +z.x '!,,!fo
7><, +sxz, + .l.X.3 + X'4 S4SO
.:ix..,, +:V<1,1z +�Xw3-)(c,-Xr,_- Xe1 So
x.1.J,+ Xi.)LT Xw3 � /Soo
Xe, +- x,2 -1- Kr3 � 12.oo
QPR� .,ao
<a)�/-- TORFJ:
Xt,Ji =SSo, Xw,=-:JS"o, XwJ :7oo
X, ,l(u XJ • X.t, ;ao
To!eP, $al,,1,jp,.. :
><,: o, ><z::. 133.33, x3 �o, ;(q= StJ
z s, ;.:1.7so
Xe, = 6Z<!, ..lie," ZFo, )(c3 = Zl(IO
M11,cirn,'zl!. z �:::,0 x, + JO.Yz r SOK.3
Z = :fl. !4, 918
(b) J,,,.� I??�� -•
� ��
S1<bject Tb
(D
©
@
@
� x, +ax. :rsx.3 :i:. 4110
4X, +.:t.Kl �7)(3
!.6000
x, + · �Xz +Lx :S. I.S110
x .J
��./2�-�·�
��M-UIUd�
:rI _
- T
X1.
i
di.
x.. - x.,
.
•
x.1-3x,. =o
Hvv1-��- .Jl,1"4
-n,,� Cgaf�;:'"�
"n'l�o�� , Pd�
� M.,l. �Zi ....-........
� � �1ar.JfAU!v..'c/J'1>1. ..,.
Aa.'o/eu/.
T - -;s:,ot. sx,. -2.)(j = 11
x, � :loo, Xz;;: i,o, � �1.,
- CPTUIM SOLIITIClt SIJtlMT - -
fltle1 Probl• z...•12 - •••
fl•l lt11••tfmn IDI 4
CbJ-=:tln Ylh• c-..J a410l1.DIZO
'4.;l.tit, v,t.. Obj toitff ClbJ VII CGrtrib••••.•
• 1 ·-- l24.Jl4] JD.0000 9729.7305
12 216.ZT6Z za.0000 �4.llt,z
al S40.S405 50.0000 Z7027.IIZ7]
continued ...

2-15
�tralnt IJIS tlKkC•>ISUrphat:; ••••
I �:) 40CIO.OOQO 0.0000· ·•
Z <•> 60DG.OOOO 4&.4165·
J l•J 150a.OOOO U1'.lS75·
4 C•J 0.0000 D.0000
s ,., 0.0000 o.oooa
....... , ZDD.1111111 1U.3Z4l+
U•az ZIIO.DDOD 16.Z162t-
....x3 151.0000 l90.540St-

J 4ao 100 0
z 4a<1 411() 200
.3 ;l.00 0 0
�
i, t.e, j = �i,1
Chapter 2/
152
IiJ = £..J�'7- JjfT"arlLc.t i "'" ,_.B. j
t/OQO ( 4500 .Cl pso ei souj .,*: ,,,
i i iSto S"too
� ....�
7Sl
O
7trkl C!JR.f = :f167, 4�o ·
�. " Pr,�·annvu,,vr..,.; rru.rk,,"· · ISJ
I,=Gd��· .
f1,;.,;,,,,·�c Z= �OX1+z.z.xl-1-?.'f�+Z6X,(f-
l,Z.00 0
i �
loo
':, jli.oo
i � .IZ..oo IZo-
s.s.
3.!:(I, +-Z.._ +I3)
0 = Sao +I1
I,-,.x'l,-= 4-flo-t-[i.
Zz rX3 = 4so-+ .L3
1j -t Xy = ,,,t�o
ci,1r"""m� :
X· 6 400, i.=S';,4L •
.I;_f:/Oo, t-��3
Io= z., = o
....
d,....4 l • t � l •300 'loo 4.SO
/dtd CAAi" .,_ t;3�.ZS"O
..:."-..
2-16

1
:/,
Xz. = 4., d
Chapter 2
X;· = Uni,(; IJ�c,1-i . J·: ,, ... IS-4
�:--=�./,;w...'r macl.-i- ,·}·.,I 2
1/= � -/,w.,.1-n-,"Jd...:. i, l /
.M11;c;..,'ze Z=- IIOX +IIKX1-too (;j._�l+)
S, f. , a
)(I + X'z. + ;J.,--J:-t .::, 8'
S $ I I ,
x, + x',. +- "'- - .,-1- = 8.
5 '7[ <71. o;.
i+� 4, cfz+ = <!f
')(I :, )(?. I i-, ·, .;;! 1'> �-> ;J...-#' � ()
y�-,
RCArl,,,,,NJ... .,. t;2 s z
><, = 5"6 , ;J_ + = 4 fu
I of
:x-, ,.,-:.
,. = o
C1
2-17

x,""
�""'' :Z =- 32 -,.
155
Chapter 2
.. � L. .,...,,a"...i·�--..,,
J<;::- 4, JS:,?., l('I: t;, JC,;_ -=.z,x7,.q,Xio"'',�z If
4L¥c,1.4,. 0
� "'k'_/,;.$cao•·d.�AAJI,¥ "'Mf". IS&(< •I : 111"'�. < � 7: sv.-. "',)
M,;,;,,,,'z, C: Z = � +x.,.+ � + Yy rX.r +l', 'f Y7
s.f.
� X ._ X3 Xy Xs- x, ",
1
I I I I I � 2o
.ic; = 4. x.. = �.> .x.,:: � J<.r"""'J � = "'.. 0
� "- (., � • ll.=- ;,,, : ';}..,. • ;/.�= 0
I I I
I I I
I I
I
I :!: IO
I �IS
�/Jl
8:01 I
'f:01 I
101•1 I
ll••l
11·.01
3:ol
�-z.
I �2..
l I �3
I I �
I I ?:4
I I �3
I ��

:
� .s
4:o I I �3
salMJ.tm: z = 'I sl,.de.rll;
X,:l, �= i,X.,==3, lr7=?
2-18

© 2017 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

•. Chapter 2
60
Let x, = Nbr. starting on day i and lasting for 7 days
Yu= Nbr. starting shift on day i and starting their 2 days off on dayj, #j
Thus, of the x1 workers who start on Monday, Yio will take T and W off, y13 will take W and Th off, and so on, as
the following table shows.
x, X: X3 x, X5 x. x,
I
2
Y1:+Yu y13+y., y14+y.,
y2-l+y25
y,s+y,.
y25+y26
Y••
y26+y27
3 y3l+y37 y35+y36 y36+y37
4 y-ll+y-17 y4l+y42 y45+y46 y46+y47
5 y5l+y57 y5l+y52 y52+y53 y53 y56 y56+y57
6 y6l+y67 y6l+y62 y62+y63 y63+y64 y64 ��
,;(;,.�.,,-�.
y67
7 y71 y7l+y72 y72+y73 y73+y74 y74+y75 y75 �'·
,
f..'"
J".Su f·•rtr '!�. " ', '-
Minimize z = x1+x�+x3+ X4+xs+xi;+xi
Each employee has 2 days off: x, = sum{j in I..7J#lYu
Mon (1) constraint: s-(y27 +y31+ y37 + y-ll+y-17+ y51+ y57 +y6l+y67 + y71)>= 12
Tue (2) constraint: s -(yl2 + y3 l + y-11+ y-12 + y5l+y52 + y6l+y62 + y7HJ72>= 18
Wed (3) constraint: s -(yl2+yl3 + y23 + y-12 + y52+y53 + y62+y63 + y72ry·73>= 20
Th (4) constraint: s -(y13ry·l4 + y23 +y24+ y2-I + y53 + y63ry·64 + y73+y7-1>= 28
Fri (5) constraint: s -(yl-l+yl5 + y24 ry·25+ y34 ry·JS + y-15+ y64 + y7-l+y75>= 32
Sat(6) constraint: s -(y15ry·J6+ y25 +y26+ y35 + y36 + y45+y46+ y56+y75>= 40
Sun(?) constraint: s -( yl6+ y26 +y27+ y36 + y37 ry·46+y47+ y56ry·57+y67)>= 40
2-19
continued

Chapter 2
n
' CJ
;
Solution: 42 employees
Starting Nbroff
On Nbr M Tu Wed Th Fri Sat Sun
M 16 i_6 -16
l
��..),,,,�
'. - '. ,._ )
Tu 8 '8
.......
8
......
Wed 8
Th 0
Fri 6
.8
,..
'"';"-]
"'
.
6
� ..:. ..e,
Sat 2 2
r:7·· -
Sun 2 ,2 2
Nbroff 10 24 22 14 10 2 2 .
Nbrat work 32 18 20 28 32 40 40
Surplus above
minimum 20 0 0 0 0 0 0
2-20

Chapter 2
Xe..,. tJbr: 6b 'M.-a-» �"'lw!;
xd= IJb.-. 1 ,d...rlxu
x,.=Nhr:1_7'-H �
x� = lld,;,)� ..,..· ft �
161
,Nl�x� z::: (ooxG+7sox,.,-12ou{tloo
e-r. Xe !:S-a11,KJ�soo,><s s s s»
s.}, X3�·S, )l,,><�,,..1,XY�I
8U x, + 'OXz + S"oX.3.,.711Xy ?:- .,_ea
Oplfn,"111: Z-,. 3({.Jflf1,"1/i1111 $
' 1(
1
=X.=I, X3=Xv=·S"
J.f.J.r)- � ,.1.
2-21
continued ...

v ,( n, U •Tr
1 3
Chapter 2
ss»; � 1·3 )( .,.,.zx +·SK+ I v«
O,el-i'm,-.: Z = 82.</0.30 �� f
Xl=loo,- X,,,:.12.s-, x,.,-=-ZZ7.o'f
"r:: J'oo I ><s � 3:/..S'I, �::: :i.s
Xe:: o
J,/e.,i ja,,w} IAIU �.' �
.1. .X, +3)(._+ �x3 + X'f 1::. ·85 (�011+ IOuj
t/e.,1 O'p�i?>..... ..rdwlrm:1
z •.J3,pJs;-,4t{/. ss:
.>(, == s rt.s« �
><1=;.tbr-. if-4.:f,-{��
l(i." N,,. 1oltnJ.1,.-H �
)(._ =- x3 = a
x,.,. ..,. /. 91 �
X.3,.N�•-1¥-(� �
'iq �"'I,,. 1,u� �
t1z =;
�1�,'16/.3S--3,3"1�S2f,2o
-,
/,j�,m,·ze z: to,too�+ 12.ooox,. + ts-0110 K.3
J./..
3
- 1>423, 7lf-0.3�
A z < �so, oao» ,,JI,.�
:t>< +-i1:><.+4X +Xy,;;, ·8S'xtoo esn..f 'l 1 (!1 aore» . II&r<c.e.. ":
x, � "bd,. '>'INI a� .-A
x,+x._+x3 �. s err ·S>t,-·•Xz--r11.3?:o
x4 � X,+:vr3-+� <tf.:u"xp-.,'"t-'2.-3'x1.:o
!LO'O
/la o '(, -,1z.00X1_+t',tqo}(3+ fdo}('f. � ( 0 '!, OtTO
400 X, + 6a" Kl.+ B'foXa +4'S1'Xi' s: Zoo, oa�
X,, X',., )(7, x., �o
X, = 339. JS" how,e s
x.,. 0
X3 :. o
x'f = /. ('l a..u•
��-
s: ..
t.
3 '7�s 2.1 . zo
3,

2-22

x,,,... //,
,,a
5 ,s, o
Ci,q,1-
J
J.
Chapter 2
1,.1 xs ... lbrf� �,..�� ,,,
xb 2 tb � .t&; � 'f"l4.�
Xn =- lb f. � � �clz-�
"'9- � -p-v.r-�
M,�o
z & /, IX5 +l·s·,r.6 + 7oxn
: + .!:!!x.w
J<"q 30
J ,/., Y =- � + X.1, + Xn -t Xw-
Xs ;i, ,/ Y
x, � . �s Y, X1:, !:: x..,, Xi. � Y.O so ""lo n
)(n � ,l,Y
Xw � ·I t'
'f � I
tUt "VM,'.'� jllM. � If(.
opt;,,""""�'
Y=-1, X. = X,-=- ·Zr)(."'.,,- x =·IJA -'W
=- �/. /2 -
X = /I, sr o-zvl.r 4'i, � It B c
Xi.j:
- -
0, (A,.S,C) ll ' ' -�
Xr, (A, t:) = //, /) �.,,;. w.u.t,, 11-, C
)( ) =- lb 9-ccrcon...io .....; Cui.Id,, 13. C
c,(8,c '
x "- /I, '1 o/mrrv(,.,;, aMJ. A,� ca,CA,�c)
� " {,t -t �B + "8c
� ... XrA + x,. C
Ye. ' 1s + ic
Ya = x;;Rt XaB + c
"?!• ��-+ 1-A + .l;11
� � 1e:+{s-t1s
l. ,'1 B c
5 4S'DOO 7.s;,11<1 0
3- 4-s; 011 f1 7r, Of1CI 0
It 0 /S-01 Otld 0
ftJ,O d0 3't111 00 o O
)('s = 80 frns, )(, = klo r,11J, -Ka=IS'd fms
Z = /43� 0011/d�
� - x;c -+ c + � c + � c
2-23

Chapter 2
continued...
2-24

-J
'?
N'R= 1,/,l/d't/ 'I na,,l,m �..; "#JA, 1-Z
!,Ip,, 1:,1,1)1,y fr.yA!. � 4.i�
ur= 1,1,,;,'d 1716f"1A ..uetflM.Jif-
Lfl = ;,1.1Id1 "J 1Ji!...u,wf"'" "fj..u-. .
LP= 1,1,t(l(f! "/, �""4Uf'.- F""",,.,,_
LT."'".1,1,//1!� f �M.C..Ul�J'e.1-
t(s""/ ;de"� �°"' ""' ?,-.);/_. �
14�,;,,,·ze z « 5of?-/{)r7o (p_f'1) +111(!-i)
-(lo f?.--t-lS-P-+ c:o:r-)-{ztl+ "3f,.,'IJ*)
- (3oA -t: 9rlls)
S,f
Chapter 2
n'J4')(/m,·ze z = /SO x, +t/fJOXz. + z Hox9 +ss-1s,
s.t.
Xq � 4fl0<7 ,c • I
.,,_ )('I � 4 Ot:J
/x� + -:iF):!S' . !1 x qooo
x, + (- . I'
.,.._ .1,Xi +·'I.S-XL + .X,3 $: ,/z.
x, � «s , x. "?: 2.r
.x3 � 2.)- , Yi, ?l O
O� .r.64irn·cfo'm 7oR,q:
· It 6.2.S
-
-oo,
..,
B � So oo XI :. :/ S /;n.s � w,,t,k
R-,. le -R ;:. s-110
x. = :2s: /ins '!"" we.• le.. .
F+ f-- p.,..,, 7110
X3
· ,,
= J('J.'J.S" ian-o
r
,,
r
..,
-
.. w�ck..
:r+ J--11"-=- "too x. ::
z
400 -fd....,.
.r.��,,11.s·o
t>J•..
ft..
· 3<sfJ. + · Y.s8::: 11/R-1 AfP-tNJ
·!otl+·SB =LR-tLPrLJ
R =NR+L'R
P= Jv'P+LP
:[.,., NJ"+LJ'
at.{ � a.M. ,,"""4:7�.
,r#
/1-= 1,1,J/-A. 1�.k 19 . 74
B � ""'/A cl)- A-torlc. J3
�i= 1,1,1µ..l!;AMAl.i.,;.J�-' �--} i=l,'Z.
Yai " bl.I/./,,.. 8 .-,.s/ �c!o.ttl,.i. t
Ma1f1m,-Z� Z= 7(�,..,.�1
)+lo(�z+�1.)
s,s. .4 =- � -t- };:i, , A-� «s»
tfp/,._.,c:!r4t,:.,.,,: Z = :/', 7//173. 'Ii' 1
B=-1&,+ Ysi., g::. 100
·;;(= 1G/l�.21, B=- o
�=- se», P= 7ot7, J" 'l<7o
continued...

98''ra,+ g9"/ � '/I ('1!,-r�,)
98'�z-+ 87�z � 'l3(�2+'J'sz)
/o''lt1,-18 ,, .!: 12-(�, ... '&,}
/O't,z+Z}sz
�/"Z(�2+Ye1). cw
�AM-
�c1� oe1r,,.
�,
Z :
:f,
/O,
srs:
.4,,,
L/S°I
J
J..J/13.
B = 7 o» 1,.,,/e;
Gas� I p-,-,..t,,..,+,..,, "'�t ,, I/
= "-111-'2.�"3,:::'2.iS'bb h
G'� !2 �c./,i,,,-=.'17!2,--t )Bi -'if1� W''
=3ta",8'1+'1t6·U- � 1nr
2-25

-a
I
Ghapter 2
x,"J· = � iJ.,ii... i. aJ/.qai,fJ/ 1o J!.:yA
w�= UnA ')�-A�
M11:xfmi1.c. '2-= �oo. w11+ 300 Alg
- Bo CX,11+ �8)
- 40 (Xu,+ X•13)
- so (x411 + X38)
176
s.u,bjeci: t-o
srefo..t,,. ·�%!& '.
,z x,11 +·I XzJI + •/IS�il � ·3 � (D·
•1 X,A + ·2 x211 r·IIS X4A .� .3 lvA@
• 3 X,A + · 3 X2,q + .a .)(3A ;:,,. ·S' lo/A(]
• I )(,;8 +- ·2 �B + •osX38 :'!: •'I Wg@
''"is+ •ZX•B -,'•OS'� � .,wB©
·3XJ8·+ -�x,8 +.7 X38 � ·3 w @8
•3 �8 + ·3 x,B + · Z X311 :S -7 Ws6)
��-·
x,1t + .x,8 ,,. 10110
XzA + Xl8 � JlQoo
x.,A + 1<.36 � a o,o
- ll'TIIUI SOWTUII SUIWIY •-
Thie: 'rcbl• Z6a--17 ··••·
flNl lt•r•tl111 Ila: tl
ObJ.ctlw Y9lue ,_, -400000.oooo
z =- :f 117, 1-3�. ss:
s= o,, I}= �J'. z, c= Jq,f'f. '"
V.rl.til• Y•lw Obj CO.ff Obj Y•I CG'!trl;······
at""' ···········,m.9999···-·zoo.oooo ···· Js�:"HM ·
d .. IOOG.0001 300.0CIOQ lOCOOO.QJ1Z
aJ at, 1000.0000 -JO.oooa -looaa.oooa
M xtl 0.0000 •JO,DIIOO ·0,0IIOQ
.d a2A 0.0000 ·40.0000 •0,0000
d zooa.0001 -4'1.00DO ·!ICIDOD.00111 a7
a.lA 3000.0000 ·50.DDOO •150000,0000 al di
1,0000 ·50,000Q ·D.0000
C..tnlnt 1111 llmc:tc·J/Surpho(•J •
i"'"' 0.0000 1090,0000- ••••••
e ccJ 1.0000 m.oaoo.
J (>J D.0000 0,0000.
4 C>J 0.000D D.0000+
S Cc) D,DDOO ZOO 0000·
6 C>J D,DODO l00:00C12+
1DD,OCIOO·
7 C•J D.0000
I C•J 10CII.DODO o aooo-
1}1, = st = o
I= rs«, I,.=- z so
� = 3'�·,"f.,):: Z.,3.79, ..d.:: II?. 'f2.
9 I•> ZOOI.OCIOD o:OOCI0-
11 l<!) 3DDO,DDDO lt.DCIOI-
.Sa4.t:.,.; '
?�(.,L., I,f()O -n,-,,.A f a.ft?/A
� /ao» Ir,-,..,,, "/ � 8.
2-26

1 :
. . -
Chapter 2
XL· :Nb.... 1y-o.tl.,tfa- � (.: i= ��'f 78
/11,n,'m,it:. z. = s-+ s-+ S'.-+ s••-
s»,
I L J T
(.-3qaro+6f{<Jf10+3o,oi,}x, + s;-
- S'
+
·SIX 910,tJ•II
(t'o,•••1"3'�000 -11,,,••J)(� + !{-s..-t= ·S"/1<4�0011
(4o,040+ 1ci.ooa) K +s.--s+ ••s-J x <1011,odo
• 3 ;, � +
( fo,ooo -:t s,o,,o) xy rs;- Sy,,. •.,., x lo� .uo
1soo(x, +Xi +xs + xy J :s;, 1001 tJt10
X11 x., iCJ , Xv .;;. o
�·;
"'I= -
"'•
"T _,
Xz -3•IY� X3 = '/,119.., Xy :!,/'/,
19
«r
Ma.'1(1°mlz e Z : ?f
s-s .
2f � J<i, -rX11
s> Jh+ XL1
rJ� X,a +Xz3
80
2-27

Chapter 2
M,-,,,..,:z.c z-=- d,+<1,+···-tq10
s.).
<1,_.-11i-b !S d;
i._.- at=]» ?:-d,:
Q,b, �cU
d, >-.o
.J;,�: .;.,. "':t '1S1/I./ i. + b .f/Z'i!o7
��!ZwlWL�W;ffe
3
X.flr+ �' � 2q 010
x4,.,.xu, .s,. 1.r-,0,0
x,r-1 Xlr-t-X�r..,.'Lvr� 3S:to
)<,, -tXz.,-t�,+:ry, >- 3.S-20
.s.41,,,;,.
Al-AZ: �s = 1760 (1,,, c... Yd)
AJ..-M: Xn;= o
A3..;.A:i.: Xzs=- o
113 �Al(: x•u,-= 1760
p1......Az, 'Ss =- 17{0
Pt�A'I: X3, '" 0 f'2....
Az.: x"s = a f'J�A'f:
X46 = ,1,0
u1- ..,10, 03.2., ao»
/JI= :ir,uo.,oa/fsa := 1760 c�-/JYa'
/l;. � .:IS".20, 113-= t76o.,A4 = 3S:l0
1)ish,,.,c.u (,e,.kr i-o ce.Ji,..).,,;. m ;,&,,, ,
Al A</,
Al .2 7
l'il 2 3
Pl 3 8
P.1t 7 �
' continued... continued...
2-28

I
°'3 �
,o ,....,.,)t
I
j
Chapter 2
I . ' II III .
200 regular
200 reserves
P1«�/rn,"%.� z .,.. T
s.e.
T "!, t,,+ t,-...,. t,3
xi.-= eff,ctu.� '6 t'.,,.;t •· 165
T � °t:i, + t:.... + -t.._3
M,·,,;,.;u. z" ·2(soo) x;+-2s (3•••>x-..
+ ·IS (6•••)1C.3 + ,18(/ooo))(y
X11 + x,..+{3-r Xz, +- �2.-t-Xi3 s; zoo
a1., + �3 + �. + 2-011
s:i .
s-oa(t-,<,),;,, ,aao{f!;XU�aoo
c" = · S + K,G .!!.l.!....3o
t;ll e ·7S +7, 'l x,.+.Y,•
t
13 " ·SS +10.z X',3 + >J3
20
t.7/ : f./ r lO .s )(ZI
3a
tn.,. t. 3 + 3./ x.L-+ Y,...
40
tl3 =- /.s; +9,l Xz3 + Y.1
=S
-=,
�/) 1"
="_ •
: ,, .J.u 2 0 .
= 8 7./�ti�
• '14(!:'oa)(t-",) +3••• ( 1-.<il.:! ·•••�"' 2zo, ood
, 91/z. (Sao)(/•",)+ ,'l'f(3ao<>) (1·1<,) + ,aoa (t-".1)
· ,3 �.004zx200,o,,
• 'f'f (.S'oo)(l·",)+·'l'lz.(300) { ,'7V(fooo)CI-'!;,)
+ tooo(t->f4J .s ,ooozxi!.IO,•••
0 :s><, �. 99
11 :$ J<', !: . 'l't
O s x3 � • '/'I
""= l<y.!:. ·'l'f
J'4w,;
3 o IM3 6•
-.. Zo - P!t>J I 'Ifw,..':f. " , 99
QJJ,W.. �-..,
Z'f. (!{" l�S"-1
asrr,a-1,,.,,,..,: *IEl'l1.q.1

--
I
---
.5
-a
-3·1.'j
-40
+- - •
0 I �
.
f'/o,,,..1- A 'lf_u.'t,,,.�.,. . 11,1
�J�a Yr"'."'"';/" .,,
/7,/--I- // effw-� = · 91.29
,3.31 $1:K'l
continued...
2-29

""'" ,,..,_
�
...
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......
-·•
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""'·""
......
1
W;. =- C..,-.� if tJok. � {/<ApS) 86
!Zt = R� ...; � «1-Af"e...,/
!<'1. = R� ...,. � a.J- � e,.,.,1
Chapter 2
- IPJIIUI IOWtlDI tlNIIIT "•
•••• •••••••••••
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PIMI he,..tl1111 lo: 16
c:1tJoc11.,. .,.,.... telnl •U190Cl,OOOO
- ALftUAJIYl aalwthn dot.cud ,t •13
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45.0000 '4K"9'9·.•"U
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w, + "'-'t
, (CJ .··..•... 0
.....0
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I?, -+ JI!:... - C-tralnt HS Sl..:kt·)ISW,..I..(•>
...,
� (�)tt( �)+'' (�•) +Zt (";.°'-)
= So R._
J (CJ
J C•>
• ' t•)
' t•)
7 (•)
11.0000
JO
.O
.D
...00
.0
.0
.1200.0000
0.0000·
0.0000
0.0000
F<., .:;. .2 S' J ,0
..... <
-.z.J,.•
w, �20 1
�
J� ..
t,
..
.J
.-.. � 2. 0 S'otd-rm:
A;rcr.rTY"e. &..tF. ,/},,.�
I I e
w; = �o. s-1 ;::.,?
w;, = � 7, 4/ K..j,r
)<ij"�Y6r. f� 1fr c '87aikWY Ii, ,trMb. J.
( /"' � 2, � '{, j =.1,2., !J, '0
�--Nb,-.lj-��.
� j, J::f,Z13,'/ .
M,;,,;.,;,c. z ::/110(.Jx,,)+1100 (.ZJ(,z)
+ 1.100 (2. lfu) + · 15®("'")
+ 6oo(4-X1,,) +900(.J )(,..)
t lo00(3Jru) +10,. (l. JCLV)
t '•o(S-'!zi) +800 csx41.)
+ PD• (4 )(31) + 'foo (z. X.Jv)
+41s,+sr,s1 +4ss.,-+
?oSy
.Su bjt!ef l:o q
4
f.x · <5" � Xa::!5 B, a lC,1j � loJ.,· IJ - ) J=1 J J·:,
.
S"o(JK,1) -,.Jo (4xl,) -1Zo(sx31) +s, =
1000
Sb(AX,z) +3• (3'1'u) +Z•C•X.11) + .s1 ,.
Aooo So (�,t,,J+Jo(3Xu)+2°.f4Jt.13)
+S3 = 'loo so ( "•O + 3o(ll(rv)+
'to(ax:,.,) +sv =.1200
All i,t,,,,,.,,/ .sj· � o

z 4 K
3 I ).5
3 .2. 7·S'
�du,,d� ....... 4,1-� �•
C«zl = /; 121, '/Pt?
continued ... .
2-30
SOLUTIONS MANUAL for Operations Research An Introduction 10th Edition
by Taha IBSN 9780134444017
Full download: http://downloadlink.org/p/solutions-manual-for-operations-
research-an-introduction-10th-edition-by-taha-ibsn-9780134444017/
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