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Exercices de programmation linéaire
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SOLUTIONS Exercice E
x1=7x2=10z=17 Exercice2
Formulationduproblème: Maximiserz=250x1+45x2 souscontraintesx1+0,2x1 ≤ 72 150x1+25x2 ≤ 10000 x1 ≤ 50 x2 ≤ 200 etx1,x2 ≥ 0
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Embed Share Share Doc x1=40x2=160z=17200 Copy Solution: 0 Link Exercice3 Add Formulationduproblème: Embed Doc Minimiserz=2x1+x2 To Copy Link souscontraintesx1+2x2 ≥ 2 Collection Readcast 4x1+3x2 ≥ 6 Comments Collections 3x1+x2 ≥ 3 Readcast ≥ 0 Share etx1,x2 CommentGo Back Solution:x1=0,6x2=1,2z=2,4
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Formulationduproblème: Maximiserz=5000x1+2000x2 souscontraintes2x1+x2 ≤ 50 x1+3x2 ≤ 25 3x1+4x2 ≤ 60 etx1,x2 ≥ 0 Solution:x1=20x2=0z=10000 Exercice5
Formulationduproblème: Minimiserz=100x1+400x2 souscontraintesx1+x2 ≥ 6 x1+2x2 ≥ 11 x1+5x2 ≥ 23 etx1,x2 ≥ 0 Solution:x1=3x2=4z=1900 Exercice6
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Ilexisteuneinfinitédesolutionsoptimalespourvuquez=x+ y=5. Exercice7
Formulationduproblème: Maximiserz=10x1+6x2+12x3 souscontraintes5x1+x2+x3 ≤ 1 x1+x2+3x3 ≤ 2 etx1,x2,x3 ≥ 0 Solution:x1=0x2=0,5x3=0,5z=9 Exercice x
Formulationduproblème: Maximiserz=2x1+1,5x2 Souscontraintes2x1+x1 ≤ 1000 x1+x2 ≤ 800 x1 ≤ 400 x2 ≤ 700 etx1,x2 ≥ 0 Solution:x1=200x2=600z=1300 Exercice e
Formulationduproblème: Maximiserz=4800C+6000R souscontraintes10C+10R ≤ 130 16C+24R ≤ 240 30C+90R ≤ 810
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15R ≥ 180 etC,R >= 0 Solution:C=9R=4z=67200 Exercice Er
Formulationduproblème: Maximiserz=30x1+12x2 souscontraintes600000x1+200000x2 ≤ 18000000 120x1+60x2 ≤ 4500 800x1+600x2 ≤ 42000 etx1,x2 ≥ 0 Solution:x1=12x2=54z=1008 Exercice E1
Formulationduproblème: Minimiserz=3,5x1+6,5x2+5x3 souscontraintesx1+x2 ≥ 15 x1+2x2+x3 ≥ 20 0,5x1+0,5x2+x3 ≥ 10 x1+3x2+2x3 ≥ 25 etx1,x2,x3 ≥ 0 Solution:x1=15,5x2=2,5x3=1z=75,5
Bibliographie: YadolahDodge, SylvieGonano-Weberet Jean-PierreRenfer(2005) Optimisationappliquée.EditionSpringer.
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