Special matching problem

Hi!
I have a theoretic problem which looks like weighted bipartite matching, but
has another constraint. I have already searched for a solutation but could
not find one.

The problem is as follows: Given n tasks and n processors, each task can run
on any processor but has an affinity a(t,p) \in N to run on a certain
processor.

I want to assign the tasks to the processors, i.e. find a mapping m: t -> p

(1) sum over a(t, m(t)) for all t is maximal
(2) for any two tasks t, t': The affinity a(t, m(t)) is not smaller than the
affinity a(t, m(t')), i.e. to the processor used by t'.

Does there exist a simple solution?

Thanks, Michael
.