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P7.4 Arithmetic-Geometric mean inequality. Consider the optimization problem minimize efit. .. ten subject to at+In = c where c is any scalar. (a) Is the above problem convex? Explain. (b) Find an optimal solution r*. (c) Use the optimal solution to prove that the arithmetic-geometric mean inequality (ajaz ... an) 1/ holds for any set of positive numbers a; > 0, i = 1, ..., n. Hint. Show that the objective value is no less than ne /" over feasible points, then use the change of variable r; = log(a;), i = 1, ...,n