Question: Let u R n be a vector such that for all ij, u i u j .The constrained optimization problem is to maximize subject to

Let uRn be a vector such that for all ij, ui uj.The constrained optimization problem is to maximize subject to x1 1.

(x1=i=1nxi )

(a) Show that this problem has a unique solution x* and give the expression of x* in terms of u (Lagrange multipliers are not needed here).

(b) Give a graphical interpretation.

Thank you for your help!

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