by Milton Harris and Artur Raviv - Faculty

and
H(Q)
L(Q)
A(Q), for Q Q B (r,p),
B pr (Q), Q B (r,p) G. The rest of
this case follows as in Case 1 above. Therefore H and L are given by (18) and (19), and the optimal
design is the same as for Case 1 above and pictured in Figure 6.
Case 5: J > Q B(r,p), J > G > Q B(p,r), and min{J,2r+r 2 s} Q K(p,r)
Since J > Q B(r,p), G < J, so H(Q) = max{A(Q),B pr(Q)} for Q G. Also, using (8), K pr(G) =
B pr(G) > A(G) = D(G), so Q K(p,r) > G. Since Q K(p,r) J and D(Q) is less steep than K rp(Q), D(Q)
K xy(Q) for Q Q K(p,r). Finally, since Q K(p,r) 2r+r 2 s, Q 4p > Q K(p,r). Therefore,
D:\Userdata\Research\Hierarchies\temp.wpd 42 February 22, 2000 (11:18AM)
(22)
(23)