This paper presents two significant applications of linear programming in breast cancer research: diagnosis and prognosis. The diagnostic system, developed using the Xcyt image analysis program, accurately distinguishes between benign and malignant breast lumps based on cellular features from fine needle aspirates, achieving 100% chronological correctness in diagnosing 131 subsequent patients. The prognostic system, a novel approach that predicts the likelihood of breast cancer recurrence, uses linear programming to construct a surface that estimates the time of recurrence. This system has an expected error of 13.9 to 18.3 months, outperforming other available techniques. The research highlights the potential of linear programming in improving the accuracy and objectivity of breast cancer diagnosis and prognosis, with implications for broader medical decision-making and machine learning applications.This paper presents two significant applications of linear programming in breast cancer research: diagnosis and prognosis. The diagnostic system, developed using the Xcyt image analysis program, accurately distinguishes between benign and malignant breast lumps based on cellular features from fine needle aspirates, achieving 100% chronological correctness in diagnosing 131 subsequent patients. The prognostic system, a novel approach that predicts the likelihood of breast cancer recurrence, uses linear programming to construct a surface that estimates the time of recurrence. This system has an expected error of 13.9 to 18.3 months, outperforming other available techniques. The research highlights the potential of linear programming in improving the accuracy and objectivity of breast cancer diagnosis and prognosis, with implications for broader medical decision-making and machine learning applications.