In: Statistics and Probability
A HW has to be assigned and evaluated in these Corona times. An Assistant with a mask will take sterilized homeworks from the Professor of the course and distribute it to the students. There are N students in the course. All the students are located in different places and since they are doing social distancing they do not go anywhere and stay at home and also do not meet any friend. The Assistant has to distribute the HW to all the students one by one. The assistant waits for the student to complete her/his homework and take it back. Student i needs xi minutes to complete the homework. Of course, it takes some time to go from one place to another and the assistant wants to minimize his time for doing this job. Therefore, he will take the HW from the Professor, go to each student exactly once and finally bring back together all the solutions (of the students) to the Professor at the very end. Please help this Assistant in this work to minimize his time for doing this duty.
Question 1. Model this problem as an IP problem. (Please clearly state that which are parameters and which are decision variables)