Breast cancer is one of the top most causes of cancer death. It is one of the malignant cancer for women in the world. It has become life-threatening among non-communicable diseases nowadays. Being female, increasing age, obesity is the main causes of breast cancer. Beside this, hormonal imbalance is the serious risk factor for breast cancer. It also develops in male body. Applying the Pontryagin’s maximum principle, the optimal control policies such as surgery and anti-cancer treatment are adopted as control measures. The target of this study is to minimize the number of cancer stem cell, tumor cell and density of estrogen as well as the associated cost of the control. We apply the optimal control strategies for this reason. Our goal is to find the strategy of preventing breast cancer transmission among cell population. The model is investigated both analytically and numerically. The analysis reveals that both the surgery and anti-cancer drug treatment could be the most fruitful way to reduce the dynamics of breast cancer.