  This paper deals with the classic radiotherapy dose fractionation problem for
cancer tumors concerning the following goals:
  a) To maximize the effect of radiation on the tumor, restricting the effect
produced to the organs at risk (healing approach).
  b) To minimize the effect of radiation on the organs at risk, while
maintaining enough effect of radiation on the tumor (palliative approach).
  We will assume the linear-quadratic model to characterize the radiation
effect and consider the stationary case (that is, without taking into account
the timing of doses and the tumor growth between them).
  The main novelty with respect to previous works concerns the presence of
minimum and maximum dose fractions, to achieve the minimum effect and to avoid
undesirable side effects, respectively.
  We have characterized in which situations is more convenient the
hypofractionated protocol (deliver few fractions with high dose per fraction)
and in which ones the hyperfractionated regimen (deliver a large number of
lower doses of radiation) is the optimal strategy.
  In all cases, analytical solutions to the problem are obtained in terms of
the data. In addition, the calculations to implement these solutions are
elementary and can be carried out using a pocket calculator.
