The Real College wants to maximize enrollment and minimize

The Real College wants to maximize enrollment and minimize costs in their phd program. With the discount rate for each student, they make $20,000 on tuition of $36,000 – 2 year program. They have around 40 full-time and 20 part-time faculty teaching in the program. Also have classroom space for 15 rooms of 30 students each. For online and in-person instruction, they cap courses at 30 students. They currently have 250 students in the program. For any profit they make, they keep 70% of the profit and give back 30% to the central University pool. As a consultant, you have been asked to apply Linear Programming using Excel Solver and determine the optimum phd student enrollment given the information above. You can make reasonable assumptions but indicate such.