Operational Research Problems
In this project, my class learned how to do operational research. We did four problems throughout the course of this project: One that was somewhat of an introduction (that we started and finished with), one that was the problem that we learned with, one that was a practice problem (where we used the knowledge we had gained from the first two problems), and one where we actually engaged with people who were supposed to be our clients (the real deal). I will be talking about the latter problem.
In this problem, we were assigned to find out how many in-state, and out-of-state students a college could accept. While doing this, we had to keep in mind a set of constraints. Here they are:
In this problem, we were assigned to find out how many in-state, and out-of-state students a college could accept. While doing this, we had to keep in mind a set of constraints. Here they are:
1. The college president wants this class to contribute at least $2,500,000 to the school after graduation. On average, the college has received $8,000 from each in-state student and $2,000 from each out-of-state student post graduation.
2. The college wants students with good grade-point average. The grades of in-state students are usually lower that out-of-state students. Therefore, the faculty wants at least as many out-of-state students as there are in-state.
3. The housing office can't spend more than $85,000 to cover vacation time costs for students in dorms. Out-of-state students are more likely to stay during vacations. In-state students cost an average of $100 each and out-of-state students cost an average of $200 each.
The college treasurer needs to minimize educational costs. Because students take different courses, teaching an in-state student costs an average of $7,200 per year and teaching an out-of-state student costs an average of $6,000 a year.
2. The college wants students with good grade-point average. The grades of in-state students are usually lower that out-of-state students. Therefore, the faculty wants at least as many out-of-state students as there are in-state.
3. The housing office can't spend more than $85,000 to cover vacation time costs for students in dorms. Out-of-state students are more likely to stay during vacations. In-state students cost an average of $100 each and out-of-state students cost an average of $200 each.
The college treasurer needs to minimize educational costs. Because students take different courses, teaching an in-state student costs an average of $7,200 per year and teaching an out-of-state student costs an average of $6,000 a year.
The strategy that my group used was to find the feasible region (area that satisfies all constraints) on a graph, find the vertices, and test them. The inequalities that my group found (using the variable i for in-state students, and o for out-of-state students) were:
1: 8,000(i)+2,000(o)>=2,500,000
2: o>i
3: 100(i)+200(o)>=850,000
4: i>=0
5: o>=0
Money Spent=(i)7,200+(o)6,000
All we had to do next was plot the constraints (NOT the money spent) on a graph, and see where all of the inequalities overlapped. That was the feasible region. After that, we found the three intersection points for the lines of the inequalities, and tested them using the money spent equation. The point that cost the least amount of money was (250,250) where x was in-state students, and y was out-of-state students. You can see our graph below. The other points, as well as the other sums of money from the money spent equation are on it.
For this project, we had roles. My role, the spokesperson, was to explain things to the client. Gaby was the facilitator, who needed to keep us on track. Gavin was the Geogebra guru, so he made the graph in Geogebra. Lastly, Elena was the documenter, who had to write everything we did as a group down.
I think that all of my group did very well with their jobs. Gavin's graph looks great, and he helped with the inequalities. Gaby kept the group on track for the whole period. Elena not only took notes, but she also typed them up and shared them with our group. I think I did a pretty good job engaging with the client, and I helped with the actual math.
I think that overall, my group worked well together very well. As I said, we all did our jobs, and we eventually did find the best recommendation (250 in-state students, and 250 out-of-state students). A challenge that we faced during this problem was staying organized. During the practice problem, we did very well with this, but I think having the client there made us all nervous (even if only a little bit). Something we could have done to solve this could have been going a bit slower, so that we could make sure everyone understood everything, and so the documenter could write everything down.
I think that my biggest strength in my role (spokesperson) was not being afraid to speak up and talk to the client. I tried to keep up a running dialogue with the client, and that really helped with their understanding of the problem (I think). Something that I think I could have done better with my job was describing and articulating my explanations. I knew the answers to a lot of their questions, but I didn't know how to put them (my answers) into words. I never knew if the explanations I had given had answered the client's questions, or just given them more.
I think that all of my group did very well with their jobs. Gavin's graph looks great, and he helped with the inequalities. Gaby kept the group on track for the whole period. Elena not only took notes, but she also typed them up and shared them with our group. I think I did a pretty good job engaging with the client, and I helped with the actual math.
I think that overall, my group worked well together very well. As I said, we all did our jobs, and we eventually did find the best recommendation (250 in-state students, and 250 out-of-state students). A challenge that we faced during this problem was staying organized. During the practice problem, we did very well with this, but I think having the client there made us all nervous (even if only a little bit). Something we could have done to solve this could have been going a bit slower, so that we could make sure everyone understood everything, and so the documenter could write everything down.
I think that my biggest strength in my role (spokesperson) was not being afraid to speak up and talk to the client. I tried to keep up a running dialogue with the client, and that really helped with their understanding of the problem (I think). Something that I think I could have done better with my job was describing and articulating my explanations. I knew the answers to a lot of their questions, but I didn't know how to put them (my answers) into words. I never knew if the explanations I had given had answered the client's questions, or just given them more.