Suppose our target is to max Pi n gi log Pi, i=1 n subject to 0 P; 1 for all i and p = 1, Pi i=1 - = qi, i = 1,...,n, is = qi, i - where q; qi 9i is known, 0 q 1 for all i, and 19 = 1. Show that pi the maximizer. Hint: argue that (i) it is without loss of generality to assume qi (0, 1); (ii) under (i), the optimal p; is an interior so the restriction 0 < pi 1 does not count.