4 Knowledge-based hierarchy A two-layer organization wants to maximize its output: max R(n) = >[F(A: U Am) - ap(A;)] + theF(A; U Am) - ap(Am) i=1 Subject to 1) tittm - 1; 2) tm = Ch[1 - F(Ai)]. i=1 Here Am is the manager's knowledge set and A; is each worker's knowledge set. t'm is the manager's time devoted to production and to to helping workers. As discussed in class, F(Z) is the cumulative density function of the knowledge content of a problem. By the downward sloping assumption of f(2), A; = [0, zu] and Am = [0, zm], where zu and 2m are the knowledge level acquired by each worker and the manager respectively. As a result, A; U Am = [0, zm]. Therefore, we can rewrite the above optimization problem as follows: max R(n) = n[F(2m) - azul + th F(2m) - azm Subject to 1) tittm