**MSC:**- 06A07 Combinatorics of partially ordered sets

<= of its elements such that for any i and any subset F of the i-th

level N_i the shadow of the |F| smallest elements of N_i w.r.t. <=

is contained in the set of the smallest |\delta(F)| elements of N_i-1,

where \delta(F) denotes the shadow of F. We consider the following

three optimization problems for P: (i) Find the maximum weight of an

ideal of given size. (ii) Find the minimum weight of an ideal generated

by an antichain of given size. (iii) Find the maximum number of maximal

elements of an ideal of given size. We provide solutions for a class

of Macaulay posets which includes all examples known so far.