  An unceasing problem of our prevailing society is the fair division of goods.
The problem of proportional cake cutting focuses on dividing a heterogeneous
and divisible resource, the cake, among $n$ players who value pieces according
to their own measure function. The goal is to assign each player a not
necessarily connected part of the cake that the player evaluates at least as
much as her proportional share.
  In this paper, we investigate the problem of proportional division with
unequal shares, where each player is entitled to receive a predetermined
portion of the cake. Our main contribution is threefold. First we present a
protocol for integer demands that delivers a proportional solution in fewer
queries than all known algorithms. Then we show that our protocol is
asymptotically the fastest possible by giving a matching lower bound. Finally,
we turn to irrational demands and solve the proportional cake cutting problem
by reducing it to the same problem with integer demands only. All results
remain valid in a highly general cake cutting model, which can be of
independent interest.
