A growing cell is characterized by the two-dimensional state vector consisting of cell volume and nuclear (chromatin) volume (mass). The state dynamics is governed by a system of linear differential equations and controlled additively by a set of genes. We assume that for the fixed cell type under consideration, the cell volume and chromatin volume at which mitosis begins is known. This point in the cell volume-nuclear volume phase plane is referred to as the target. For certain types of malignant cells the target is reached in the minimum time possible, given all the constraints of the system. The time-optimal requirement forces the active genes to be ‘ fully on ’, and the resulting slight increase from the ‘ normal on ’ activity level is shown to cause a significant decrease in the generation time of the cell type.