8. (10 points) Suppose our target is to
max g: logpi
subject to 0 <
p: ≤1for all i and Sp =1,
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where qi is known, O < qi < 1 for all i, and C1 qi = 1. Show that pi = qi, i = 1, ... the maximizer. Hint: argue that (i) it is without loss of generality to assume q; € (0, 1); (ii) under (i), the optimal p; is an interior so the restriction 0 ≤ pi ≤ 1 does not count. 程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com