Problem 1 A university is attempting to adjust its student profile in all courses based on a new metric that estimates the course difficulty based on previous results. The focus is to minimize the total difficulty for all students, considering several criteria and limitations, as shown below: There are a total of 10 courses, spread throughout the week (schedule in white). In order to deal with occupation issues and idle capacity in the campus, the university has estimated a minimum and maximum level of students per day (green). Also, each course provides a certain number of credits (orange). In order to assure a balanced workload, the university has also estimated a minimum and a maximum number of credits that should be offered (blue). One must also consider the classroom capacities, which limits how many students can occupy the same classroom (yellow). Finally, the table also provides the estimated difficulty scores (gray) from the new methodology. a) Formulate a linear programming problem accounting for all constraints and trying to minimize objective function. b) What are the courses/classes occupations and how many vacancies are there? c) What days of the week is the campus most empty and what days are more crowded? d) Considering that the average student typically averages in 5 credits, what Is the average difficulty score per student? e) Based on the results and the overall criteria, create a ranking of the courses/classes that the university should focus on expanding capacity for future years. f) What would happen if the university increased the minimum credit for all students to be at least 800 credits? How would that change the solution? The implementation and solution of this problem can be based on your preferred optimization package (Example: LINGO, Excel, MATLAB, GAMS, etc). You must add the implementation code/spreadsheet to your