This paper presents two medical applications of linear programming for breast cancer diagnosis and prognosis. The diagnostic system uses cellular features from fine needle aspirates to distinguish between benign and malignant breast lumps, achieving 100% accuracy in diagnosing 131 patients. The system, called Xcyt, analyzes images of cells and computes 30 features for each nucleus, enabling accurate diagnosis without surgical biopsy. The prognostic system predicts the likelihood of cancer recurrence, providing better information for treatment planning. It handles both censored and recurring cases, with an expected error of 13.9 to 18.3 months. The system uses linear programming to construct a recurrence surface, minimizing errors in predictions. The diagnostic and prognostic systems have been tested on 569 patients, with the diagnostic system achieving 97.5% accuracy and the prognostic system showing promising results. The systems are used in clinical practice, with the diagnostic system providing probability estimates for malignancy and the prognostic system offering survival predictions. The research also explores extensions of the recurrence surface approximation, including implicit RSA and nonlinear time functions, improving predictive accuracy. The study highlights the potential of linear programming in medical diagnosis and prognosis, with applications beyond breast cancer, including other types of cancer. The results demonstrate that linear programming-based systems can achieve high accuracy and reliability in diagnosing and predicting breast cancer outcomes.This paper presents two medical applications of linear programming for breast cancer diagnosis and prognosis. The diagnostic system uses cellular features from fine needle aspirates to distinguish between benign and malignant breast lumps, achieving 100% accuracy in diagnosing 131 patients. The system, called Xcyt, analyzes images of cells and computes 30 features for each nucleus, enabling accurate diagnosis without surgical biopsy. The prognostic system predicts the likelihood of cancer recurrence, providing better information for treatment planning. It handles both censored and recurring cases, with an expected error of 13.9 to 18.3 months. The system uses linear programming to construct a recurrence surface, minimizing errors in predictions. The diagnostic and prognostic systems have been tested on 569 patients, with the diagnostic system achieving 97.5% accuracy and the prognostic system showing promising results. The systems are used in clinical practice, with the diagnostic system providing probability estimates for malignancy and the prognostic system offering survival predictions. The research also explores extensions of the recurrence surface approximation, including implicit RSA and nonlinear time functions, improving predictive accuracy. The study highlights the potential of linear programming in medical diagnosis and prognosis, with applications beyond breast cancer, including other types of cancer. The results demonstrate that linear programming-based systems can achieve high accuracy and reliability in diagnosing and predicting breast cancer outcomes.