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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

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