Overview
Our task for this engagement was to find the best combination of watercolor and pastel paintings for the artist to sell so that he could make the most money. We were given certain constraints such as: the artist could only create 16 paintings total, the materials for the pastel costs $5 while the watercolor costs $15, and that you would get more money from the selling the watercolor than the pastel. To be exact, the profit for each pastel painting is $40, while the profit for each watercolor painting is $100.
Solution
The first thing that my group and I did was read the problem while paying attention mainly to the constraints. We created inequality's for each of the constraints, which were: x>=0, y>=0, x+3y>=36, x+y<=16. (X is pastel while Y is watercolor) We explained these inequalitys to our client. We explained to him what each constraint was, and showed how we converted it into an inequality. After we convinced him that creating these inequalities were necessary, we changed them into equations so that geogebra could identify all of the points of the vertices. All we had to do to change the inequalities into equations was to have and equal sign. The constraints turned into: X=0, Y=0, X+3y=36, X+Y=16. We then graphed these newly formed equations using Gegebra.
Graph
Solution continued
After we graphed these points in Geogebra, we first had to explain what Geogebra was to our Client. We explained that it was a program that graphed points for us so that it would be more accurate and neat. We explained that the points A, B, C, and D that is shown in the graph is the vertices of the feasible region. We explained that the feasible region is the area of all the possibility's of combinations of Pastel and Watercolor paintings. This took a while to explain because our client was still confused why only that part of the graph was possible. We explained that we had to keep in mind all of the constraints, therefore, only the shaded in region was possible. After we made this graph we knew that the next step was to find out which combination would make the artist the most money, We also knew that in order to find the maximum profit we had to test out all of the vertices of the feasible region. We used the equation that we made earlier for the profit which was: 40p + 100w = profit. (P stands for pastel and W stands for watercolor) We tested out each of the vertices points coordinates, by plugging them into the equation. The coordinates for point A: (0,12) point B: (6,10) point C: (16,0) point D (0,0). After we did the math for each of the points, we came up with each of the profits for each point. Point A's profit = $1,200. Point B's profit = $1,240. Point C's profit = $640. Point D's profit = $0. The answer to this whole problem is that the combination of pastel and watercolor paintings that would make the most money is: 6 pastels, and 10 watercolors (point B). We know this is the best possible combination because we tested out each vertex of the feasible region, and point B created the most amount of money.
Group Roles
The people in my group was Me, Ethan, Ricky, and Chloe. I was the facilitator, Ethan was the documentor, Ricky was the spokesperson, and Chloe was the Geogebra Guru. Although we each had specific roles that we did, we all participated in every aspect in order to find a solution to this problem. I did not really have to facilitate at all because my group did an excellent job at staying focused and on task the whole time. I helped to document as well by writing down all of the equations. I also helped to be the spokesperson by helping to explain everything to our client, and lastly, I also helped Chloe with Geogebra.
Reflection
I believe that every person in my group did an amazing job. We all participated and tried our best to convince our client that point B was the best solution. We came out very successful in the end. I think that what I did really well for the client engagement, I created all of the inequalities/equations for the constraints, and I also answered and explained a lot to our client. I helped Chloe plot everything in Geogebra, tested out all of the vertices of the feasible region, and helped to convince our client. Chloe did her job very well by plotting everything in Geogebra and also by helping to explain things to our client. Ricky did his job well by helping to explain everything to our client, he also helped to come up with constraints and helped with Geogebra. Ethan did an amazing job. He explained ALOT to our Client, helped create the inequalities for the constraints, tested out all of the vertices of the feasible region, and helped me to convince our client that point b is the best possible combination.
My group worked really well together. We all contributed, and a reason why we worked so well together is because we were all comfortable with each other. The only challenge my group had was that at first it was kind of awkward with our client and we didn't say much. Once we dived into solving the problem however, we became more comfortable and did an excellent job explaining and convincing. What my group did really well with was that we all worked our best to conduct our roles, while also helping each-other with each others. If I were to do this again, I would probably solve the problem faster so that we could have more time to convince our client. Like I said earlier, my role was to be a facilitator and I didn't need to facilitate at all because my group was very focused and on task. I think my biggest strength was that I helped with every single role and didn't just focus on mine. I've been a facilitator many times and I feel that I really am a pro at it now. I think in the future I would want to try out different roles to give me a more variety of learning.
My group worked really well together. We all contributed, and a reason why we worked so well together is because we were all comfortable with each other. The only challenge my group had was that at first it was kind of awkward with our client and we didn't say much. Once we dived into solving the problem however, we became more comfortable and did an excellent job explaining and convincing. What my group did really well with was that we all worked our best to conduct our roles, while also helping each-other with each others. If I were to do this again, I would probably solve the problem faster so that we could have more time to convince our client. Like I said earlier, my role was to be a facilitator and I didn't need to facilitate at all because my group was very focused and on task. I think my biggest strength was that I helped with every single role and didn't just focus on mine. I've been a facilitator many times and I feel that I really am a pro at it now. I think in the future I would want to try out different roles to give me a more variety of learning.