We are interested in optimizing the co-administration of two drugs for some acute myeloid
leukemias (AML), and we are looking for in vitro protocols as a first step. This issue can
be formulated as an optimal control problem. The dynamics of leukemic cell populations in
culture is given by age-structured partial differential equations, which can be reduced to
a system of delay differential equations, and where the controls represent the action of
the drugs. The objective function relies on eigenelements of the uncontrolled model and on
general relative entropy, with the idea to maximize the efficiency of the protocols. The
constraints take into account the toxicity of the drugs. We present in this paper the
modeling aspects, as well as theoretical and numerical results on the optimal control
problem that we get.