Two medical applicationso f linear programminga re described in this paper. Specifically, linear programming-basemd achine learning techniques are used to increase the accuracy and objectivity of breast cancer diagnosis and prognosis. The first applicationt o breast cancer diagnosisu tilizes characteristicso f individualc ells, obtainedf rom a minimallyi nvasive fine needle aspirate,t o discriminateb enign from malignantb reast lumps. This allows an accurated iagnosisw ithout the need for a surgical biopsy. The diagnostic system in current operation at University of Wisconsin Hospitals was trained on samples from 569 patientsa nd has had 100%c hronologicalc orrectnessi n diagnosing1 31 subsequentp atients.T he second application,r ecentlyp ut into clinical practice, is a method that constructs a surface that predicts when breast cancer is likely to recur in patients that have had their cancers excised. This gives the physician and the patient better informationw ith which to plan treatment,a nd may eliminate the need for a prognostic surgical procedure. The novel feature of the predictive approach is the ability to handle cases for which cancer has not recurred (censored data) as well as cases for which cancer has recurred at a specific time. The prognostic system has an expected error of 13.9 to 18.3 months, which is better than prognosis correctness by other available techniques.