Problem Statement:

The two Woo siblings own a small bakery that only works with cookies, they only make two kinds plain and iced. The Woos need to decided how many to make of each, the final combination has to have the greatest profit. Each dozen of plain cookies requires 1 pound of cookie dough and 0.1 hour of preparation. Each dozen of iced cookies requires 0.7 pound of cookie dough, 0.4 pounds of icing, and 0.15 hour of preparation. The Woo’s have some constraints they only have 110 pounds of cookie dough, 32 pounds of icing, oven space for 140 dozen cookies (1680 cookies), and 15 hours for cookie preparation. They want to make as much as profit as they can, each plain dozen of cookies sells for $6.00 and cost $4.50 to make ($1.50 profit), each iced dozen of cookies sells for $7.00 and costs $5.00 to make ($2.00 profit). The essential question is “How many dozens of each kind of cookie should the Woo siblings make to have their profit as high as possible?”. To begin to answer the questions find one combo of dozens plain and iced cookies that will fit every restraint, then figure out the profit the Woos will make.

Process Description:

When I first read the cookie problem ratios immediately came to mind, I thought “Why not have for every 2 dozen plain there will be 4 iced dozen?”. This thought never actually got tested, my group decided to dive in and test out multiple combinations. Our first combination were 70 dozen plain and 28 dozen iced cookies, this gave us a total of $616, after reviewing our equation we found a miscalculation. Instead of multiplying the profit from each dozen we multiplied the actual cost per dozen cookies, this gave us a much higher profit but did not fit the restraints. After finding our error we decided to test out the same numbers again, our total profit from 70 dozen plain cookies and 28 dozen iced cookies was $161.

Solution(s):

Our final solution that the class found was 30 dozen plain cookies and 80 dozen iced, that came out to a total profit of $205. You would think that having all the dozens of cookies being iced, while still meeting the requirements, would give the Woos the most profit. Speaking from a practical standpoint yes that might work in most situations, but since there are so many restraints, for example the time that the Woos have is a very big problem. It takes 0.15 hour to make one dozen cookies, when only having 15 hours to bake you can only make a certain amount. Finding a happy medium will give you the most the profit, in our graph ,after finding the section that meet all restraints, we as a class found that the most iced cookies you could make was 80 dozen and the most the plain cookies would be about 50. The 30 plain and 80 iced is a happy medium for these cookies, this to me seems to be the most profitable combination because of the business standpoint this problem was giving to us and all the requirements that had to be meet and kept.

Self Assessment and Reflection:

At first glance this word problem seemed very easy, but because I usually overthink things ,especially in math, it became difficult as my group progressed. As we got deeper into this world problem and we started plugging in the numbers, I started to confuse myself. I decided to use my habits of a mathematician, once I started over I decided to start small. Once I started small and conjectured and test, I found a lot of combinations to fit the restraints of the problem. When my group and I collaborated we found even more combinations, when listen to each other we can correct or even elaborate on each others equations. If i were to give myself a grade out of 20, I would give myself a 19. I think I deserve a 19/20 because I feel because if i would’ve used my habits of mathematician, I wouldn’t of confused myself with my equations. For the following project I will be sure to look over and use my habits in the

The two Woo siblings own a small bakery that only works with cookies, they only make two kinds plain and iced. The Woos need to decided how many to make of each, the final combination has to have the greatest profit. Each dozen of plain cookies requires 1 pound of cookie dough and 0.1 hour of preparation. Each dozen of iced cookies requires 0.7 pound of cookie dough, 0.4 pounds of icing, and 0.15 hour of preparation. The Woo’s have some constraints they only have 110 pounds of cookie dough, 32 pounds of icing, oven space for 140 dozen cookies (1680 cookies), and 15 hours for cookie preparation. They want to make as much as profit as they can, each plain dozen of cookies sells for $6.00 and cost $4.50 to make ($1.50 profit), each iced dozen of cookies sells for $7.00 and costs $5.00 to make ($2.00 profit). The essential question is “How many dozens of each kind of cookie should the Woo siblings make to have their profit as high as possible?”. To begin to answer the questions find one combo of dozens plain and iced cookies that will fit every restraint, then figure out the profit the Woos will make.

Process Description:

When I first read the cookie problem ratios immediately came to mind, I thought “Why not have for every 2 dozen plain there will be 4 iced dozen?”. This thought never actually got tested, my group decided to dive in and test out multiple combinations. Our first combination were 70 dozen plain and 28 dozen iced cookies, this gave us a total of $616, after reviewing our equation we found a miscalculation. Instead of multiplying the profit from each dozen we multiplied the actual cost per dozen cookies, this gave us a much higher profit but did not fit the restraints. After finding our error we decided to test out the same numbers again, our total profit from 70 dozen plain cookies and 28 dozen iced cookies was $161.

Solution(s):

Our final solution that the class found was 30 dozen plain cookies and 80 dozen iced, that came out to a total profit of $205. You would think that having all the dozens of cookies being iced, while still meeting the requirements, would give the Woos the most profit. Speaking from a practical standpoint yes that might work in most situations, but since there are so many restraints, for example the time that the Woos have is a very big problem. It takes 0.15 hour to make one dozen cookies, when only having 15 hours to bake you can only make a certain amount. Finding a happy medium will give you the most the profit, in our graph ,after finding the section that meet all restraints, we as a class found that the most iced cookies you could make was 80 dozen and the most the plain cookies would be about 50. The 30 plain and 80 iced is a happy medium for these cookies, this to me seems to be the most profitable combination because of the business standpoint this problem was giving to us and all the requirements that had to be meet and kept.

Self Assessment and Reflection:

At first glance this word problem seemed very easy, but because I usually overthink things ,especially in math, it became difficult as my group progressed. As we got deeper into this world problem and we started plugging in the numbers, I started to confuse myself. I decided to use my habits of a mathematician, once I started over I decided to start small. Once I started small and conjectured and test, I found a lot of combinations to fit the restraints of the problem. When my group and I collaborated we found even more combinations, when listen to each other we can correct or even elaborate on each others equations. If i were to give myself a grade out of 20, I would give myself a 19. I think I deserve a 19/20 because I feel because if i would’ve used my habits of mathematician, I wouldn’t of confused myself with my equations. For the following project I will be sure to look over and use my habits in the