Fundraiser
Overview
The Artist's Dilemma was a problem we had to complete with the supervision of a "client". Our client was a student from Cal State San Marcos named Robert. For this problem, we had to come up with a recommendation that will make the artist the most money while still meeting the constraints. My team had to come up with the best recommendation while only spending $180 for supplies, the max paintings that can be created is 16, watercolor materials cost $15 and pastel costs $5. The profit of the pastel is $40 and the profit of the watercolor is $100.
To obtain the best-possible recommendation, we created a Feasible Region on Geogebra and found the intersection points on the graph. The intersection points were: (0,12) (6,10) (16,0). Watercolor was dubbed as the y- axis and pastel was the x- axis.
Constraints
Max spending: $180 ~ 5p + 15w ≤ 180
Max paintings: 16 ~ p + w ≤ 16
Pastel costs $5
Watercolor costs $15
Pastel profit: $40
Watercolor profit: $100 ~ Profit = 40p + 100w
We tested the intersection points with the profit equation to see which would be the best-possible recommendation.
(0,12) (6,10) (16,0)
40(0) + 100(12) 40(6) + 100(10) 40(16) + 100(0)
0 + 1200 240 + 1000 640 + 0
$1200 $1240 $640
We found that the intersection point (6,10) is the best-possible recommendation because it is the farthest point from the origin and it is on the very edge of the constraints. For example, if I try the points next to the intersection, the profit won't be as much or it will be outside the constraint.
(5,10) (6,11)
40(5) + 100(10) 40(6) + 100(11)
200 + 1000 280 + 1100
$1200 $1380
As you can see, the coordinates (5,10) are within the constraints, but the profit isn't higher than the profit of $1240 from the intersection point (6,10). The point (6,11) has a higher profit than the coordinate (6,10), but it is outside the constraint. This proves that (6,10), in translation 6 pastels and 10 watercolors, is the best-possible recommendation in the feasible region.
The Artist's Dilemma was a problem we had to complete with the supervision of a "client". Our client was a student from Cal State San Marcos named Robert. For this problem, we had to come up with a recommendation that will make the artist the most money while still meeting the constraints. My team had to come up with the best recommendation while only spending $180 for supplies, the max paintings that can be created is 16, watercolor materials cost $15 and pastel costs $5. The profit of the pastel is $40 and the profit of the watercolor is $100.
To obtain the best-possible recommendation, we created a Feasible Region on Geogebra and found the intersection points on the graph. The intersection points were: (0,12) (6,10) (16,0). Watercolor was dubbed as the y- axis and pastel was the x- axis.
Constraints
Max spending: $180 ~ 5p + 15w ≤ 180
Max paintings: 16 ~ p + w ≤ 16
Pastel costs $5
Watercolor costs $15
Pastel profit: $40
Watercolor profit: $100 ~ Profit = 40p + 100w
We tested the intersection points with the profit equation to see which would be the best-possible recommendation.
(0,12) (6,10) (16,0)
40(0) + 100(12) 40(6) + 100(10) 40(16) + 100(0)
0 + 1200 240 + 1000 640 + 0
$1200 $1240 $640
We found that the intersection point (6,10) is the best-possible recommendation because it is the farthest point from the origin and it is on the very edge of the constraints. For example, if I try the points next to the intersection, the profit won't be as much or it will be outside the constraint.
(5,10) (6,11)
40(5) + 100(10) 40(6) + 100(11)
200 + 1000 280 + 1100
$1200 $1380
As you can see, the coordinates (5,10) are within the constraints, but the profit isn't higher than the profit of $1240 from the intersection point (6,10). The point (6,11) has a higher profit than the coordinate (6,10), but it is outside the constraint. This proves that (6,10), in translation 6 pastels and 10 watercolors, is the best-possible recommendation in the feasible region.
Group Roles
My group consisted of Ashley Seymour, Eli Steria and Faris Livingstone. Ashley was the facilitator and she did very well as a facilitator, no one was out of hand and everyone was focused to the best of their abilities. She could've participated more in the discussion so she can share her thoughts and opinions, but I figured that if we all stepped back then she could've spoke. Eli was the spokesperson and he did well, when our client asked him about the problem he was able to explain what he heard. He could improve by listening the whole time so he doesn't have to rely on us to repeat the information back. Faris was the GeoGebra expert and he did a great job putting together the graph and explaining what was on the graph. He could improve by labeling the graph because it wasn't labeled so it wasn't very clear which line was which and what the axis were. I was the documenter and I feel I did a good job taking on the role because I feel I was able to take down everything that was important. I could improve by making my notes more organized and clear, and repeating this information back to the group.
Reflection
I would like to celebrate that Ashley was listening the whole time and was able to keep everyone on track, she collaborated and listened. Eli for being able to repeat the information that Faris and I gave out, he collaborated and listened. Finally, Faris for staying organized by creating an organized graph for the feasible region. I want to celebrate myself for taking down all the important information and the work that my group did, I started small. Our group worked very well together by collaborating ideas and listening to each other. It was challenging trying to translate the recommendation to our client because he didn't understand it very well so we had to keep thinking of different ways to translate the ideas. We overcame it by giving him examples of what we did and explaining what the feasible region is. My biggest strength as a documenter was writing down all the information that was needed for our group to be successful. I could grow in this role by being more organized with my notes so that it could be easier to read. I feel that with more practice, I could accomplish this improvement to make it the best that it can be.
My group consisted of Ashley Seymour, Eli Steria and Faris Livingstone. Ashley was the facilitator and she did very well as a facilitator, no one was out of hand and everyone was focused to the best of their abilities. She could've participated more in the discussion so she can share her thoughts and opinions, but I figured that if we all stepped back then she could've spoke. Eli was the spokesperson and he did well, when our client asked him about the problem he was able to explain what he heard. He could improve by listening the whole time so he doesn't have to rely on us to repeat the information back. Faris was the GeoGebra expert and he did a great job putting together the graph and explaining what was on the graph. He could improve by labeling the graph because it wasn't labeled so it wasn't very clear which line was which and what the axis were. I was the documenter and I feel I did a good job taking on the role because I feel I was able to take down everything that was important. I could improve by making my notes more organized and clear, and repeating this information back to the group.
Reflection
I would like to celebrate that Ashley was listening the whole time and was able to keep everyone on track, she collaborated and listened. Eli for being able to repeat the information that Faris and I gave out, he collaborated and listened. Finally, Faris for staying organized by creating an organized graph for the feasible region. I want to celebrate myself for taking down all the important information and the work that my group did, I started small. Our group worked very well together by collaborating ideas and listening to each other. It was challenging trying to translate the recommendation to our client because he didn't understand it very well so we had to keep thinking of different ways to translate the ideas. We overcame it by giving him examples of what we did and explaining what the feasible region is. My biggest strength as a documenter was writing down all the information that was needed for our group to be successful. I could grow in this role by being more organized with my notes so that it could be easier to read. I feel that with more practice, I could accomplish this improvement to make it the best that it can be.