**Core Concept**
Invasive breast cancer often requires a multidisciplinary treatment approach, including local therapy to manage the tumor itself. The goal of local therapy is to remove the tumor and prevent recurrence by addressing any potential microscopic disease in the surrounding tissue.

**Why the Correct Answer is Right**
The most appropriate local therapy for this patient's invasive breast cancer is mastectomy. This is because the tumor is palpable and 1 cm in size, indicating a need for complete removal of the affected breast tissue. In cases where the tumor is small and in situ, breast-conserving surgery (lumpectomy) with radiation may be an option. However, given the invasive nature of this tumor, mastectomy is the preferred choice to ensure complete removal of the cancer and minimize the risk of recurrence.

**Why Each Wrong Option is Incorrect**
**Option A:** Lumpectomy is often used for small, in situ tumors, but it is not the best choice for invasive cancer due to the risk of leaving behind microscopic disease.
**Option B:** Simple mastectomy is a type of breast-conserving surgery that removes only the affected breast tissue, but it is not the most comprehensive approach for invasive cancer.
**Option D:** Radiation therapy alone is not sufficient to treat invasive breast cancer, as it does not address the tumor itself.

**Clinical Pearl / High-Yield Fact**
When considering local therapy for breast cancer, it's essential to evaluate the tumor's size, stage, and histology to determine the most appropriate approach. In general, mastectomy is preferred for larger or invasive tumors, while breast-conserving surgery with radiation is suitable for smaller, in situ cancers.

**Correct Answer:** C.