1. maximiser 1000x1+700x2+400x3+200x4
    sous les contraintes (1) x1 0 (2) x2 0 (3) x3 0 (4) x4 0 (5) x1 40 (6) 1.5x1+1.5x2+1.5x3+1.5x4 420 (7) 1.5x1+0.75x2+0.375x3 120
  2. Oui réalisable; oui, de base (intersections des 4 équations correspondant aux contraintes (1), (2), (3) et (4)).
  3. Oui réalisable; oui, de base (intersections des 4 équations correspondant aux contraintes (3), (5), (6) et (7)).
  4. (Les lettres A à M montrent les solutions de base réalisables)
    A       ¯Equations 1, 2, 3 et 4: x=[0,0,0,0]  z=0
    B Equations 1, 2, 3 et 6: x=[0,0,0,280]  z=56000
    C Equations 1, 2, 4 et 6: x=[0,0,280,0]  z=112000
     Equations 1, 2, 4 et 7: x=[0,0,320,0]   non-r'ealisable
     Equations 1, 2, 6 et 7: x=[0,0,320,-40]   non-r'ealisable
     Equations 1, 3, 4 et 6: x=[0,280,0,0]   non-r'ealisable
    D Equations 1, 3, 4 et 7: x=[0,160,0,0]  z=112000
    E Equations 1, 3, 6 et 7: x=[0,160,0,120]  z=136000
    F Equations 1, 4, 6 et 7: x=[0,40,240,0]  z=124000
    G Equations 2, 3, 4 et 5: x=[40,0,0,0]  z=40000
     Equations 2, 3, 4 et 6: x=[280,0,0,0]   non-r'ealisable
     Equations 2, 3, 4 et 7: x=[80,0,0,0]   non-r'ealisable
    H Equations 2, 3, 5 et 6: x=[40,0,0,240]  z=88000
     Equations 2, 3, 6 et 7: x=[80,0,0,200]   non-r'ealisable
     Equations 2, 4, 5 et 6: x=[40,0,240,0]   non-r'ealisable
    I Equations 2, 4, 5 et 7: x=[40,0,160,0]  z=104000
    J Equations 2, 4, 6 et 7: x=[13.33,0,266.66,0]  z=120000
    K Equations 2, 5, 6 et 7: x=[40,0,160,80]  z=120000
     Equations 3, 4, 5 et 6: x=[40,240,0,0]   non-r'ealisable
    L Equations 3, 4, 5 et 7: x=[40,80,0,0]  z=116000
     Equations 3, 4, 6 et 7: x=[-120,400,0,0]   non-r'ealisable
    M Equations 3, 5, 6 et 7: x=[40,80,0,160]  z=128000
     Equations 4, 5, 6 et 7: x=[40,-80,320,0]   non-r'ealisable



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On 22 Oct 2009, 15:56.