A mathematical puzzle where you have to optimize a certain objective function (maximize profit, minimize cost).
A puzzle with strong mathematical contents, where you have to optimize a certain objective function. Standard goals are
to maximize the profit,
to minimize the cost,
to identify / analyze / describe the corresponding extremal situations.
Roughly speaking, optimization problems may be classified into
combinatorial (optimization concerning discrete scenarios)
continuous (optimization over the reals)
stochastic (optimization with probabilistic input)