You are the Program Coordinator for Computer Engineering program in a university. You will need to assign courses to the professors in your program. However each professor has different background and has different level of experience in teaching each course. So, you asked each professor to submit the time required them to prepare each class and the data you received is presented below: Professor Programming Database Algorithms Network 1 3.2 1.2 2.8 2 2.1 2.3 2.3 3 4 2.1 4.3 (Academicians... they all submitted precise times) Operating Systems 2.4 3 2.8 Web Application 2.6 1.5 1.3 3.2 3.5 3.3 You will write a BIP to find the best assignment that minimizes the total preparation time for all professors. There are some rules you will need to consider. 1. Each course should be assigned to one professor. 2. Each professor can teach at most 2 courses. 3. Maximum time spend on course preparation for any professor shouldn't exceed 5 hours. 4. Database and Operating Systems should not be taught by the same professor. 5. Operating Systems and Web Application course should be taught by the same professor (=if OS is assigned someone, Web Application should also be assigned) 6. If any of the professors is not teaching Programming or Database, he/she cannot teach neither Network or Algorithms. 7. The professor who is teaching Algorithms, should also teach either Programming or Web application. Define decision variables, parameters, give the sets for indexes. Write your model using variables and parameters