Question

5.1. Explain the difficulties that will be encountered if Lagrange multipliers are used with problems involving nonnegative variables.

Answer 1

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As we consider an optimazahisa problem with constraints. The problem is solved by using the containat to express one variable in terms ut. the other. hence reducing the dimensionally of me problem. Sometimes it is not convenient, or even possible to perform such a reduction of demensionality. مدحه كذا لم و لدی بیا له ده M problems navolve constraints. There are often resmictions on the rawes that can be assumed by the variables concerned. For ex. The anount of money in one's portfolio or me. concentration of a chemical species must be non nequtive Each consmints is extersedni - Fcx, y, z ) = the basic poble ar sf a consbaint can be 0 obtimization minimize ormaximize fcx, y, z) Subject to constraint FCA 4, 2) = 0 S. Langranian function Zcn, , 2, 2) = fin,1, 2) + F(x, y, z) . a is known as I lagrarte multiplier

I Langrange multipliers is a genene. method tha is effective in solving a wide variety of problems it may not always be possible tone variable in terms of others. The method of Lagrangins is very usefull in more more general problems involving an arbitary number of independent variable or consta into.