We discuss some of the problems Noah had to face when he established his
famous bagel business; Noah had to decide how many bagels of each flavor
should be produced in each of his bakeries, subject to space, production
and flavor popularities constraints. Noah's goal was to find solutions
that maximize his revenue (the Revenue problem) while guaranteeing satisfaction
to his customers (the Balancing problem).
Noah showed that both problems are NP-hard. He then looked at some special
cases, where each of these problemscan be solved optimally in polynomial
time. Finally, he found a nearly optimal solution for the Revenue problem
that paved his road to success.