Cover Letter
What was the central problem of this unit?
Central Problem:
In this unit, we had to try to find the maximum profit Abby and Bing Woo could make by baking a combination of plain and frosted cookies.
In order to do so we had to first define the constraints of the problem, and the variables we would use to represent them. We developed the concept of variables in Homework 2, “High School Letters”, and kept building on that foundation throughout the unit. The idea of constraints was introduced in “Picturing Cookies” Part I.Here’s an example of variables and constraints we used for the big problem:
Variables:
- 'P' is the number of plain cookies baked
- 'I' is the number of iced cookies baked
- '$' is the profit made by baking
Constraints:
- Maximum cookie dough usable
- Maximum icing usable
- Maximum Prep time usable
- Maximum oven space available for all cookies baked
We then needed to explore the concept of a “feasible region”, or an area of a graph that satisfied all the above constraints at the same time. We developed this concept first in “Picturing Cookies” Part II.
With the “feasible region” mastered, we could find a “profit line” that would reveal the combination of plain cookies and iced cookies baked to return different profits. Using the idea that profit lines would have the same “slope”, or incline of the line, we could try to find the specific point, or points that meet the constraints and fall on the profit line bringing about the best profit. We developed our profit line concept in “Profitable Pictures”, and never looked back from there.
In this particular problem, the highest profit point fell on the intersection of two lines, so we needed to find a point that would satisfy both equations. I chose to use a substitution method, but there’s a number of methods students could choose to use. The problem “Rock ‘n Rap” introduced this concept of using the profit line to find the maximum profit combination.
Putting it all Together:
Using all the concepts above, we then tried to solve the big problem in “Baker’s Choice Revisited”, the in class assessments, and take home assessment. By doing so, we were able to develop a procedure that worked for us when trying to solve a linear programming type problem.
In this unit, we had to try to find the maximum profit Abby and Bing Woo could make by baking a combination of plain and frosted cookies.
In order to do so we had to first define the constraints of the problem, and the variables we would use to represent them. We developed the concept of variables in Homework 2, “High School Letters”, and kept building on that foundation throughout the unit. The idea of constraints was introduced in “Picturing Cookies” Part I.Here’s an example of variables and constraints we used for the big problem:
Variables:
- 'P' is the number of plain cookies baked
- 'I' is the number of iced cookies baked
- '$' is the profit made by baking
Constraints:
- Maximum cookie dough usable
- Maximum icing usable
- Maximum Prep time usable
- Maximum oven space available for all cookies baked
We then needed to explore the concept of a “feasible region”, or an area of a graph that satisfied all the above constraints at the same time. We developed this concept first in “Picturing Cookies” Part II.
With the “feasible region” mastered, we could find a “profit line” that would reveal the combination of plain cookies and iced cookies baked to return different profits. Using the idea that profit lines would have the same “slope”, or incline of the line, we could try to find the specific point, or points that meet the constraints and fall on the profit line bringing about the best profit. We developed our profit line concept in “Profitable Pictures”, and never looked back from there.
In this particular problem, the highest profit point fell on the intersection of two lines, so we needed to find a point that would satisfy both equations. I chose to use a substitution method, but there’s a number of methods students could choose to use. The problem “Rock ‘n Rap” introduced this concept of using the profit line to find the maximum profit combination.
Putting it all Together:
Using all the concepts above, we then tried to solve the big problem in “Baker’s Choice Revisited”, the in class assessments, and take home assessment. By doing so, we were able to develop a procedure that worked for us when trying to solve a linear programming type problem.