How many of each kind?
Big Question: How many dozens of cookies should Abby and Bing make so their profit is as high as possible?
1.) Self - Assessment and Reflection
The past few weeks in math, we have been working on solving the real big question which is, “How Many of Each Kind?”. From this problem, I have learned more about what inequalities mean. Inequalities are used inorder to find the difference in size, and circumstances. I have been able to experience the process of being able to plug in Numbers in order to recieve your profit. Also while using the amount of oven space, plain and icing had eventually helped too find the total amount within the profit. I feel that I deserve out of 20 I would say 15 because I had worked alone on this problem along with my group in the end we all contributed and made corrections to the ones that needed to be changed. Out of the 10 Habits of a Mathematician I feel that I had mostly incorporated was by starting small, stayed organized, and lastly I had looked for patterns. I felt that I had started small while attempting this big question in order to come across the answer for the amount of iced and plain cookies, along with the prep time, oven space, and the oven prep. I had felt very organized throughout the process of finding the prep time, oven prep, and oven space, I had been able to not get lost within my work went step by step with organization in order to be able to go back and communicate to my group of the process that I had to come across in order to answer this big question. Before beginning the process I approached the problem by finding any patterns in order to be able to continue on finding the answers for the iced and plain cookies, oven prep, the amount of oven space, the amount of batter used, the time used, icing used, and lastly the profit.
2.) Problem Statement
There are bakers who are making plain and iced cookies, in which are needed to find out the amount of profit. In addition, the job was finding the profit by using the different materials used. There were constraints for the amount of dough, amount of icing, preparation time, and lastly the amount of oven space. Our job had been to find out the amount of plain and iced cookies that they had been able to make inorder to get the highest profit. Towards the beginning of this project, everyone had been given a chart to fill out in which had allowed everyone to figure out the amount of iced and plain cookies that had been made in order to find out the total amount of profit made. As a class everyone had been able to find different inequalities in order to use for the process in order to calculate the amount of money, time, and profit. Everyone also had eventually graphed the different inequalities in order to grasp the feasible region in which had given everyone an idea of the different kinds of numbers that would give us the maximum profit.
3.) Process Description
I had approached this problem by first starting out small by figuring out as many combinations as possible then I had found out the amount of profit, I had done this by using the equation for profit which was Profit=$1.5(Plain)+2(Iced), $1.50(150)+$2(0)=225. I feel that my group members and I could’ve possibly been able to attempt the problem as a whole, instead of being on a different part of the problem or not having the comparison of answers as the other group members. Having to go back and attempt the problem to make any corrections was some what difficult, although in the end my group members and I ended up comparing answers not many corrections were needed, although I hope that next time my group and I can at least try to work more as a whole. Eventually in class we had been able to compare within the other tables in which everyone had graphed the inequalities to see if it had been the highest possible number. I have a feeling that the chart had been the most helpful, useful tool to come across while solving this overall big question.
4.) Solutions
The highest solution found within my group members and I was that the bakery would make 29 plain cookies for $1.50 per dozen and would make 80 iced cookies for $2.00 per dozen. The bakery had made 202 along with while staying in the constraints provided. They would make 111 dozens of cookies (140) had been the maximum. You then, substitute all the coordinates that were used while graphing into the equation 1.5(x)+2(y)=profit, (29,80) makes the most profit.
Big Question: How many dozens of cookies should Abby and Bing make so their profit is as high as possible?
1.) Self - Assessment and Reflection
The past few weeks in math, we have been working on solving the real big question which is, “How Many of Each Kind?”. From this problem, I have learned more about what inequalities mean. Inequalities are used inorder to find the difference in size, and circumstances. I have been able to experience the process of being able to plug in Numbers in order to recieve your profit. Also while using the amount of oven space, plain and icing had eventually helped too find the total amount within the profit. I feel that I deserve out of 20 I would say 15 because I had worked alone on this problem along with my group in the end we all contributed and made corrections to the ones that needed to be changed. Out of the 10 Habits of a Mathematician I feel that I had mostly incorporated was by starting small, stayed organized, and lastly I had looked for patterns. I felt that I had started small while attempting this big question in order to come across the answer for the amount of iced and plain cookies, along with the prep time, oven space, and the oven prep. I had felt very organized throughout the process of finding the prep time, oven prep, and oven space, I had been able to not get lost within my work went step by step with organization in order to be able to go back and communicate to my group of the process that I had to come across in order to answer this big question. Before beginning the process I approached the problem by finding any patterns in order to be able to continue on finding the answers for the iced and plain cookies, oven prep, the amount of oven space, the amount of batter used, the time used, icing used, and lastly the profit.
2.) Problem Statement
There are bakers who are making plain and iced cookies, in which are needed to find out the amount of profit. In addition, the job was finding the profit by using the different materials used. There were constraints for the amount of dough, amount of icing, preparation time, and lastly the amount of oven space. Our job had been to find out the amount of plain and iced cookies that they had been able to make inorder to get the highest profit. Towards the beginning of this project, everyone had been given a chart to fill out in which had allowed everyone to figure out the amount of iced and plain cookies that had been made in order to find out the total amount of profit made. As a class everyone had been able to find different inequalities in order to use for the process in order to calculate the amount of money, time, and profit. Everyone also had eventually graphed the different inequalities in order to grasp the feasible region in which had given everyone an idea of the different kinds of numbers that would give us the maximum profit.
3.) Process Description
I had approached this problem by first starting out small by figuring out as many combinations as possible then I had found out the amount of profit, I had done this by using the equation for profit which was Profit=$1.5(Plain)+2(Iced), $1.50(150)+$2(0)=225. I feel that my group members and I could’ve possibly been able to attempt the problem as a whole, instead of being on a different part of the problem or not having the comparison of answers as the other group members. Having to go back and attempt the problem to make any corrections was some what difficult, although in the end my group members and I ended up comparing answers not many corrections were needed, although I hope that next time my group and I can at least try to work more as a whole. Eventually in class we had been able to compare within the other tables in which everyone had graphed the inequalities to see if it had been the highest possible number. I have a feeling that the chart had been the most helpful, useful tool to come across while solving this overall big question.
4.) Solutions
The highest solution found within my group members and I was that the bakery would make 29 plain cookies for $1.50 per dozen and would make 80 iced cookies for $2.00 per dozen. The bakery had made 202 along with while staying in the constraints provided. They would make 111 dozens of cookies (140) had been the maximum. You then, substitute all the coordinates that were used while graphing into the equation 1.5(x)+2(y)=profit, (29,80) makes the most profit.
Iced Cookies
Plain Cookies
Below is given the different components that my group and I had came across which is a graph.
Below is given a chart
The Homies, Plain Cookies 29, Iced Cookies 80, Batter Used 84, Icing Used 32, Time Used 14.8, Oven Space 108, Profit of Plain Cookies 42, Profit of Iced Cookie 160,Total Profit 202.
The Homies, Plain Cookies 29, Iced Cookies 80, Batter Used 84, Icing Used 32, Time Used 14.8, Oven Space 108, Profit of Plain Cookies 42, Profit of Iced Cookie 160,Total Profit 202.