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Cancer therapy options are directed at eradicating cancerous cells. Unfortunately, cancer treatments may also damage healthy cells. The result of this damage is side effects of the treatment. It is desirable to maintain the side effects below an acceptable threshold. This goal can be facilitated by enforcing an upper bound on the expected number of treatments a patient may receive during her/his therapy. In this paper, an appropriate therapeutic policy for a mutated mammalian cell cycle is devised. This policy mitigates the side effects of the therapy by bounding the expected number of treatments received by a patient.