3. School Applications (20 pts) Niranjan, Pooja, and Surya all want to get a PhD degree. They are applying to some of the most esteemed schools in the country as well as the #1 school in innovation, ASU. They have ranked in order their top 3 schools. The 6 universities have also ranked who their top candidates are. Both sides want to end up with their highest preference. How can we find a way to make the optimal match so both sides maximize their objective? Niranjan 1 MIT 2 Stanford 3 ASU Pooja 1 Stanford 2 Berkeley 3 UCLA Surya 1 ASU 2 CalTech 3 MIT 1 2 3 Stanford Pooja Surya Niranjan MIT Surya Niranjan Pooja Berkeley Niranjan Pooja Surya ASU Niranjan Surya Pooja UCLA Pooja Niranjan Surya CalTech Surya Pooja Niranjan i. Develop an algorithm to do the matching. Describe it here. ii. Set up the linear program to determine matches. iii. Where will Niranjan, Pooja and Surya go? How happy are the universities? show this in excel and attach solver