  In this paper, we study an optimal control problem for a two-dimensional
Cahn-Hilliard-Darcy system with mass sources that arises in the modeling of
tumor growth. The aim is to monitor the tumor fraction in a finite time
interval in such a way that both the tumor fraction, measured in terms of a
tracking type cost functional, is kept under control and minimal harm is
inflicted to the patient by administering the control, which could either be a
drug or nutrition. We first prove that the optimal control problem admits a
solution. Then we show that the control-to-state operator is Fr\'echet
differentiable between suitable Banach spaces and derive the first-order
necessary optimality conditions in terms of the adjoint variables and the usual
variational inequality.
