Question: Let 1, . . . , n be positive scalars with Pn i=1 i = 1. Use a Lagrangian multiplier to solve the problem min

Let 1, . . . , n be positive scalars with Pn i=1 i = 1. Use a Lagrangian multiplier to solve the problem min nX i=1 ixi nY i=1 xi i = 1, xi 0 i. Use the result of the above optimization to establish the inequality Qn i=1 xi i Pn i=1 ixi for a set of positive scalars xi, i = 1, . . . , n

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