Optimasi adalah suatu aktivitas untuk mendapatkan hasil terbaik di dalam suatu keadaan yang diberikan. Tujuan akhir dari aktivitas tersebut adalah meminimumkan usaha (effort) atau memaksimumkan manfaat (benefit) yang diinginkan. Metode pengali Lagrange merupakan metode yang digunakan untuk menangani permasalahan optimasi berkendala. Pada penelitian ini dianalisis karakteristik dari metode pengali Lagrange sehingga metode ini dapat menyelesaikan permasalahan optimasi berkendala. Metode tersebut diaplikasikan pada salah satu contoh optimasi berkendala untuk meminimumkan fungsi objektif kuadrat sehingga diperolehlah nilai minimum dari fungsi objektif kuadrat adalah -0.0403. Banyak masalah optimasi tidak dapat diselesaikan dikarenakan kendala yang membatasi fungsi objektif. Salah satu karakteristik dari metode pengali Lagrange adalah dapat mentransformasi persoalan optimasi berkendala menjadi persoalan optimasi tanpa kendala. Dengan demikian persoalan optimasi dapat diselesaikan.   Optimization is an activity to get the best results in a given situation. The ultimate goal of the activity is to minimize the effort or maximize the desired benefits. The Lagrange multiplier method is a method used to handle constrained optimization problems. This study analyzed the characteristics of the Lagrange multiplier method with the aim of solving constrained optimization problems. The method was applied to one sample of constrained optimization to minimize the objective function of squares and resulted -0.0403 as the minimum value of the objective quadratic function. Many optimization problems could not be solved due to constraints that limited objective functions. One of the characteristics of the Lagrange multiplier method was that it could transform constrained optimization problems into non-constrained ones. Thus the optimization problem could be resolved.

Heart disease is one of the leading causes of death in Indonesia. The high number of deaths from heart disease is caused by the lack of cardiologists, the lack of public awareness of conducting regular heart health checks and the poor lifestyle of patients. So we need an application that can make it easier for users to detect heart disease early and independently. In this study, the aim is to build an application using the website-based Bayes Theorem method as a tool for diagnosing coronary heart disease. In this application, patients do not have to wait long for treatment by a doctor, but it can be an alternative to anticipate treatment quickly and precisely. How to use this application, the admin inputs questions in the form of symptoms that will be answered by the user, then the system will process all user answers using the Bayes theorem method and the system will issue output in the form of diagnostic results in the form of heart disease and various solutions. This application uses a Web programming language and Php & Mysql as a database. The system that has been built can assist patients in knowing the type of heart disease that is being suffered by the patient and according to the analysis of heart disease experts.