A 

In an alternative reality, I considered letting each student define post-facto the percentage contribution to their grade for each of the graded activities in a given course. These activities are: homework, a term project, a mid-term exam, and a final exam. However, I have a rather twisted mind, and have made things a little bit more complicated by adding the following stipulations:

• homework can account for up to 25% of the grade, but must be at least 5% of the grade;
• the term project can account for up to 25% of the grade, but must be at least 5% of the grade;
• the mid-term and final must each account for between 10% and 40% of the grade but cannot account for more than 70% of the grade when the percentages are added up;
• the project and final exam grades may not collectively constitute more than 50% of the grade.

Let’s assume that you were my student and that your grades in these activities were 75, 94, 85, and 92, respectively.

• How would you formulate an LP model to maximize your numerical grade?
• Implement it using Excel and Solver.
• Produce the analysis reports in Solver (Answer, Sensitivity, Limits) and analyze the results.
• Based on the Solver reports information, is there anything you would request me to improve your final grade?

PROBLEM B

Higher education, particularly in the United States, is facing major strategic challenges regarding course and degree completion rates, as well as overall college retention. Across all types of four-year institutions, of those students starting bachelor degree programs in 2001, only 36% completed them within four years (U.S. Dept. of Education, 2009, College Board Advocacy & Policy Center, 2010). The numbers have improved considerably in the last six or seven years but there is still a long way to go. The emergence of data science and its application in higher education, in the aftermath of the success of these disciplines and technologies in science and business, has started to provide new tools for addressing this national challenge. Learning analytics stands at the forefront of these data driven initiatives. The goal of learning analytics is to uncover hidden patterns in educational data and use those patterns to attain a better understanding of the educational process, assess student learning and make predictions on performance.

Starting in 2017, the Sturla Foundation, through its New Initiatives in Higher Education (NIHE) program, aims to advance the field of Learning Analytics by exploring issues related to scaling this technology across all of higher education. The foundation will fund Learning Analytics projects through yearly RFPs, allocating a fixed amount of money to cover all proposals selected in the yearly round.

The Sturla Foundation intends to use the following methodology to select projects that receive funding in the yearly round.

• All projects receive an initial screening and only acceptable projects are considered for budget allocation (e.g. projects cannot receive more than $1M in funding. Any projects above that mark are rejected)
• Acceptable projects are assessed by the foundation based on their innovation, social interest, and their feasibility of completion. A score from 1 to 5 is assigned to each project, where 1 is the lower bound and 5 is the upper bound.
• If the total yearly funds allocated by the foundation is less than the sum of the budgets of all projects, then a subset of projects is selected. The selection criterion is based on maximizing the sum of the individual scores of the selected projects.
• Selected projects are fully funded (there is no partial funding)
• As much as possible of the total allocated funds for the year must be disbursed among the selected projects.

The foundation has allocated a total of $8M for 2017, and through the current RFP has received 20 acceptable proposals with the following budgets, assigning to them the following scores (see table below)

As an analyst working at the Sturla Foundation, you are requested to develop a model to optimize the allocation of the total yearly funds across selected projects among the 20 acceptable proposals received in 2017.

• Formulate the optimization model.
• Implement it using Excel and Solver.

(Hint: you should use the LP/MIP engine in Solver to produce your results)

Proposal #	Requested budget	Score
1	500	1
2	200	3
3	900	5
4	600	2
5	400	3
6	800	4
7	450	5
8	550	1
9	350	1
10	600	5
11	500	2
12	470	4
13	720	3
14	420	5
15	950	4
16	380	1
17	310	2
18	520	1
19	500	1
20	400	5

Make sure that you select the “LP/MIP engine” in Solver before solving the model and producing the reports