Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with $n$ states, subject to provocation with $m$ chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.

的增殖在体外癌细胞的群体通过用线性细胞周期模型描述$n$ 国家，受到挑衅 $米$化学治疗化合物。考虑将恒定药物暴露的线性组合最小化，将系统的稳定性用作约束以确保稳定或缩小的细胞群。主要结果涉及识别冗余化合物，以及所有暴露非零情况下的显式解决方案。在正交情况下，每种药物作用于细胞周期的单个不同阶段，导致算术平均值和几何平均值之间的经典不等式。此外，还展示了如何通过使用线性可逆变换将一般情况转换为正交情况来解决一般情况。结果用两个实例说明，分别对应于两种和三种化合物的联合治疗。