The fundraiser - operational research
A college came to us and asked to help them figure out how many students they could admit from in-state and how many from out of state. There were many requirements to make sure they stayed within their budget. The president wanted $2,500,000 from the class when they graduated, and in-state students gave$8,000 and out of state students gave $2,000. The staff also wanted a class with a good GPA. In-state students grade’s are lower than those of out of state students. The school couldn’t spend more than $85,000 on vacations for the students to stay in the dorms. In-state students costed $100 for each vacation, and out of state students costed $200. The college wanted to spend the least amount of money they could, and our task was to figure out how they could do so.
Obtaining the Best Recommendation
1. Find the inequalities/constraints
To do this, you take the written constraints and make them into inequalities.
Constraints (i: in state, o: out of state)
1. Find the inequalities/constraints
To do this, you take the written constraints and make them into inequalities.
Constraints (i: in state, o: out of state)
- Contribution after graduation: $2,500,000 ≤ $8,000i + $2,000o
- Grade point average: i ≤ o
- Housing/utilities during vacation: $85,000 ≥ $100i + 200o
2. Input them into Geogebra
After finding the inequalities, we inputted them into geogebra as the equations of lines rather than inequalities. This makes the graph easier to work with and easier to understand. I input the inequalities as lines, label them on the graph, and label the x- and y-axis.
After finding the inequalities, we inputted them into geogebra as the equations of lines rather than inequalities. This makes the graph easier to work with and easier to understand. I input the inequalities as lines, label them on the graph, and label the x- and y-axis.
3. Find the feasible region
The feasible region is all of the points that will work with the inequalities. To find the feasible region, you must figure out if it will be below (less than) or above (greater than) the line based on the inequalites. If it's greater than, then it's above the line. If the inequality is less than, it's below the line.
The feasible region is all of the points that will work with the inequalities. To find the feasible region, you must figure out if it will be below (less than) or above (greater than) the line based on the inequalites. If it's greater than, then it's above the line. If the inequality is less than, it's below the line.
Notice that there are now three points on the corners of the feasible region. Those are called the vertices.
Vertices:
Vertices:
- A: (235.71, 307.14)
- B: (283.33, 283.33)
- C: (250, 250)
4. Test the verticesThe vertices are the intersection points of the lines. You always want to test the vertices of the feasible region first. They are the closest to the outside (so they will either be the maximum or the minimum). Since the values are representing students and you can’t have part of a student, you have to round them all down to keep them in the feasible region.
Vertices (rounded):
Vertices (rounded):
- A: (235, 307)
- B: (283, 283)
- C: (250, 250)
5. Label everything!
Make sure everything (lines, equations, feasible region, x-and y-axis, graph title) is labeled so someone who didn’t do the project will understand it.
Make sure everything (lines, equations, feasible region, x-and y-axis, graph title) is labeled so someone who didn’t do the project will understand it.
There were four roles assigned to the group: facilitator, spokesperson, geogebra guru, and documenter. Adam was the spokesperson, Erik was the geogebra guru, Carson was the documenter, and I was the facilitator. For my role, I was in charge of the group. I made sure we stayed on task and completed what we were asked to do.
I thought our client engagement went pretty well. We came up with the best possible answer and our client seemed convinced. We were able to quickly figure out how to solve the problem, so we had more time to explain it to our client. After we explained what was required to our client, we were able to spend time discussing other options, which helped us to better understand the problem at hand. I think we used the habit of a mathematician “Collaborate and Listen” really well. We were able to work together well, and we shared all of our ideas and discoveries as well. This also helped us while we were explaining the problem to our client. We all got a chance to talk, so it wasn’t listening to one person going on and on. Something Adam did well as the spokesperson was that he knew what was going on and was able to clearly explain it to the clients. Something Erik did well was that he knew how to use geogebra and was able to successfully make the graph and not waste a lot of time trying to figure it out. Something Carson did well as the documenter was he knew how to format all of the inequalities and he wrote them all down correctly. My biggest strength was that I was able to successfully lead my group and we got the problem finished quickly.
Overall, I think we worked really well together. We were able to share our ideas, and everyone was on the same page and knew what we were doing, so that was good. I think that we all knew what we were doing before we started the problem helped a lot, and we were all clear on how to solve the problem. We didn’t have any major disagreements, which was good. A challenge we had was that everyone was trying to do everyone else’s roles. We all wanted to do everything, and we kind of took over each other’s roles at different times. To overcome this challenge next time, I think we should clarify the roles and makes sure everyone knows what they’re supposed to be doing.
I think my biggest strength as the facilitator is that I’m a natural leader. I think this helped me a lot. Something I can improve on as the facilitator is trying not to come off as so bossy. I think the way I word things makes it sound bossy, even though I’m not trying to be. Overall, I think everyone in my group did a great job and we completed the problem successfully!
I thought our client engagement went pretty well. We came up with the best possible answer and our client seemed convinced. We were able to quickly figure out how to solve the problem, so we had more time to explain it to our client. After we explained what was required to our client, we were able to spend time discussing other options, which helped us to better understand the problem at hand. I think we used the habit of a mathematician “Collaborate and Listen” really well. We were able to work together well, and we shared all of our ideas and discoveries as well. This also helped us while we were explaining the problem to our client. We all got a chance to talk, so it wasn’t listening to one person going on and on. Something Adam did well as the spokesperson was that he knew what was going on and was able to clearly explain it to the clients. Something Erik did well was that he knew how to use geogebra and was able to successfully make the graph and not waste a lot of time trying to figure it out. Something Carson did well as the documenter was he knew how to format all of the inequalities and he wrote them all down correctly. My biggest strength was that I was able to successfully lead my group and we got the problem finished quickly.
Overall, I think we worked really well together. We were able to share our ideas, and everyone was on the same page and knew what we were doing, so that was good. I think that we all knew what we were doing before we started the problem helped a lot, and we were all clear on how to solve the problem. We didn’t have any major disagreements, which was good. A challenge we had was that everyone was trying to do everyone else’s roles. We all wanted to do everything, and we kind of took over each other’s roles at different times. To overcome this challenge next time, I think we should clarify the roles and makes sure everyone knows what they’re supposed to be doing.
I think my biggest strength as the facilitator is that I’m a natural leader. I think this helped me a lot. Something I can improve on as the facilitator is trying not to come off as so bossy. I think the way I word things makes it sound bossy, even though I’m not trying to be. Overall, I think everyone in my group did a great job and we completed the problem successfully!