The Cookie Problem
1. Self-Assessment and Reflection:
Through this problem, I learned how to graph inequalities and find a feasible region for certain constraints. For this problem, we worked in our table groups, and my group had six people, which made it kind of hard for us to get our ideas out in the open. Working with so many people in the group, made me realize that I need to speak up and and contribute, while at the same time listen to other people’s ideas. It was a little difficult to have group discussions, because everyone was so focused and independent in their work. For this activity, I think I deserve a 20 out 25 because even though I did participate in the conversation, I didn’t really come up with the different amounts of plain and iced cookies to find the one that would get the most profit and still fit all the constraints. One Habit of a Mathematician I think I’ve utilized is Be Systematic, because when I would see if a point fit in the constraints, I would go down the list of inequalities to see if it fit within the constraints. Another Habit of a Mathematician I conquered was Stay Organized, because when testing out the points, there are many inequalities to see if the point works, so if I didn’t stay organized, it would be confusing and hard to solve the problem. The last Habit of a Mathematician I accomplished was Conjecture and Test, because I had to guess how much each type of cookie, and then test to see if it was the most profit and worked within the constraints.
2. Problem Statement:
The problem is asking you to find the most number of plain cookies and the most number of iced cookies you can make, that will give the Woo’s the most profit, while still fitting within the specific constraints. You can use multiple numbers that will give you a profit and fit in the constraints, but you always have to ask yourself: can I make more? When doing this problem, there were a lot of components used. Equations are a big part in this problem, because you had to try and stay in the constraints and use different numbers. We also made a graph and chart, where we could see where the highest constraints were, which helped because then we could go back and try go get the biggest profit, based on the constraint lines on the graph
3. Process Description:
When we began this project, nobody really knew how to start it. I began by re-reading the problem and simplifying it in my head. The next day in class, I kind of kept quiet and listened to what my group members had come up with, when I got home I started to go more in depth with the problem, and began to understand what it was asking. The next day, my group members had already started the problem, but luckily, I knew what they were talking about. After we figured out some equations for the constraints, we used a computer program called Desmos, which when we put in the equations, and it graphed it for us. It gave us a better visual for where the constraints were, and the points that we could not go past. We figured out our maximum profit that we could get, through Desmos, and the certain constraints.
4. Solution:
To find my solution, I began by trying a different range of equations. Once I found a reasonable equation, I began to test, to see if it was correct. After we tried many different equations, the next day in class, we made graphs/charts, and from there we tested the points. Since those points fit in the constraints, those points became our solution. My solution is correct and complete, because it shows the correct inequalities shaded, that were feasible and in the constraints. When we tested the points, I made sure to write it down, and mark it on the graph, so later I could go back and look at the page. If you test the points out, you will also see that it makes you the most profit, and fits in the constraints, giving you the most profit as possible.
Through this problem, I learned how to graph inequalities and find a feasible region for certain constraints. For this problem, we worked in our table groups, and my group had six people, which made it kind of hard for us to get our ideas out in the open. Working with so many people in the group, made me realize that I need to speak up and and contribute, while at the same time listen to other people’s ideas. It was a little difficult to have group discussions, because everyone was so focused and independent in their work. For this activity, I think I deserve a 20 out 25 because even though I did participate in the conversation, I didn’t really come up with the different amounts of plain and iced cookies to find the one that would get the most profit and still fit all the constraints. One Habit of a Mathematician I think I’ve utilized is Be Systematic, because when I would see if a point fit in the constraints, I would go down the list of inequalities to see if it fit within the constraints. Another Habit of a Mathematician I conquered was Stay Organized, because when testing out the points, there are many inequalities to see if the point works, so if I didn’t stay organized, it would be confusing and hard to solve the problem. The last Habit of a Mathematician I accomplished was Conjecture and Test, because I had to guess how much each type of cookie, and then test to see if it was the most profit and worked within the constraints.
2. Problem Statement:
The problem is asking you to find the most number of plain cookies and the most number of iced cookies you can make, that will give the Woo’s the most profit, while still fitting within the specific constraints. You can use multiple numbers that will give you a profit and fit in the constraints, but you always have to ask yourself: can I make more? When doing this problem, there were a lot of components used. Equations are a big part in this problem, because you had to try and stay in the constraints and use different numbers. We also made a graph and chart, where we could see where the highest constraints were, which helped because then we could go back and try go get the biggest profit, based on the constraint lines on the graph
3. Process Description:
When we began this project, nobody really knew how to start it. I began by re-reading the problem and simplifying it in my head. The next day in class, I kind of kept quiet and listened to what my group members had come up with, when I got home I started to go more in depth with the problem, and began to understand what it was asking. The next day, my group members had already started the problem, but luckily, I knew what they were talking about. After we figured out some equations for the constraints, we used a computer program called Desmos, which when we put in the equations, and it graphed it for us. It gave us a better visual for where the constraints were, and the points that we could not go past. We figured out our maximum profit that we could get, through Desmos, and the certain constraints.
4. Solution:
To find my solution, I began by trying a different range of equations. Once I found a reasonable equation, I began to test, to see if it was correct. After we tried many different equations, the next day in class, we made graphs/charts, and from there we tested the points. Since those points fit in the constraints, those points became our solution. My solution is correct and complete, because it shows the correct inequalities shaded, that were feasible and in the constraints. When we tested the points, I made sure to write it down, and mark it on the graph, so later I could go back and look at the page. If you test the points out, you will also see that it makes you the most profit, and fits in the constraints, giving you the most profit as possible.
Plain Cookie Design:
Iced Cookie Design: