Decision Yariables: xijit: Binary yariable indicating whether course i(i=1,,100) is assigned to classroom j (j=1,,20) at slot t(t=1,,15), where 1 if assigned, 0 otherwise. Parameters: ci: Exam Capacity in classroom j ai: Number of students in course i ei1,i2: Number of common students between course i1 and i2 Using the notation given above: a) Express the set of constraints that each course should have its exam only once and in a single classroom. b) Write the constraints that exams for courses indexed 1 and 99 cannot be scheduled at the same time. c) Assuming that each course can only have its exam in a single classroom, express the soft constraint that the number of students in a course cannot exceed the capacity of the assigned classroom. You max need to define new variables for this. d) Write an obiective function that minimizes the total capacity exceeded by classrooms, e) Write an obiective function that minimizes the total exceedance of classroom capacities, assuming that each exam for a course is assigned to a single classroom