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Ofshore vessels sup
the air trans
CoordinatingCiobanuSd. Chiri ă AțSd. Tîrlescu
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IntroThe activity of experienced an development de
economic growtRomania's involvinternational trinternational to
They are s
the specific chair transport, with charactermeans of transcertain items oincreasing impo
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Propose
The padress is to
number of ahelicopters the mission of Training so the totaconsumed bhelicopters,
together, t
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Categorieso transportequipment
Transport possibilities in arace
Necessaryo transport
One airplane One
helicopter
Fuel (tonnes ! " #t most "$
Food (%g !&& "&& #t least '!&&
unition(tonnes
" $ #t least "!
)quipment(pc*
"&& !&& #t most "$&&
aterials(pc*
$&& +&& #t most ,"&&
Consumptiono -ight hourson a means o
transport
! hours . hours///
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Ne0t1 2e 2ill present a mathematical
model o linear programmingproblem through 2hich 2e candetermine the number o hours
required*
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("
*
**
* * * * * * * * * * * * * * * * ** *
linear programmingproblem
numbers 1***1
3('
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• Determine the number of airplanes andhelicopters needed to fulll the mission, sothe total number of ight hours consumed byplanes and helicopters , taken together, to beminimal.
4olution: We note with the numberof airplanes and with ! the number ofhelicopters necessary to accomplish themission.
• "rom the data of the problem result thefollowing canonical linear program:
• #$% f#x%&x()y&min.
•
#*%
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("
**
*
* * * * * * * * * * * * * * * * * * *
HE LINEAR
PROGRAMMING PROBLEM
1***16&
06&1 y6&(7
3('
(03!08.y3min
C#NONIC#
9 9IN)#;O
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THE GEOMETRICAL INTE
LINEAR PROGRAMS
VARIABLE
?ettinoptimal s
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@e construct the polthe system ("1 represenobtained by ta%ing into a3 (equal into the system @e discover that poi
smallest distance rom t(4x+5y!"
d m
O
<
;
C! 0 8 " y A " $ 3 & ( '
! 0 8 " y
A
' ! 3 & ( "
" 0 8$ y A " ! 3& ( 7
" 0 8 ! y A " $ 3 &
( !
$ 0 8 + y A
, " 3 & ( .
EEE
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The distance rom O(&1& to t
!08.yA3& is :
d3 3 1unde %3
4o 3%d
#s a result3%
Observation: O
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A'!3A7!
!8"3'!33
dm33
4o1 the solution
is 0 G 7 airplanes and
helicopters
min 3 7! 87.3 '
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;
;articular cases:'H i one o the sides o the polygonis parallel 2ith line 1then it 2ill besatised one o the ollo2ingreations:
3i3'1"1***1m
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" HI the polygon ; is
unbounded ( has points to theinnit
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7H I polygon ; is reduced to apoint1 ma0imum and minimum othe unction have the same value*
The practical problems o thistype are meaningless
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#ibliography
Collection o applied
mathematicsproblems(Coordonator#cad* N* Teodorescu