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PDF Method of Lagrange Multipliers

Lagrange multiplier method is a technique for finding a maximum or minimum of a function F(xyz) subject to a constraint (also called side condition) of 

  • Quelle est la signification économique du multiplicateur de Lagrange ?

    Pour ecrire le Lagrangien, il faut bien prendre soin de transformer la contrainte sous la forme g(x, y) ≥ 0 et alors le Lagrangien est L = f + λg.
    Dans le premier cas, il faut réécrire la contrainte R − p1x1 − p2x2 ≥ 0.
    Le Lagrangien est alors L = U(x1,x2) + λ (R − p1x1 − p2x2).

  • Comment calculer le multiplicateur de Lagrange ?

    En économie, le multiplicateur de Lagrange permet de déterminer une situation optimale (par exemple comment maximiser son profit, minimiser ses dépenses, ou encore maximiser bien-être) sous une contrainte quelconque (budget limité, bien-être minimum requis).

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