ENCYCLOPEDIA PROJECT
Description
For this project, we each chose a mathematical topic such as linear programming, radical functions, linear equations etc. After we were assigned them, we had to research the topic and find jobs that use it, the definition, the skills needed to be able to use it, and an example of how it is used. After we finished that, we had to make a presentation out of it such as a poster board, or slideshow.
Linear Programming by Max Jaye
Definition: According to Merriam-Webster, linear programming is, “a mathematical method of solving practical problems (as the allocation of resources) by means of linear functions where the variables involved are subject to constraints”(Merraim-Webster).
Refined definition: Linear programming is a way to project or decide outcomes of things by using restricted variables such as money, time, size, amount, etc.
Careers that use linear programming: Professions that use linear programming include being a dental assistant, doctor, pilot, business manager, or a zookeeper(ehow1). This concept can be used to estimate the amount of medicine, food, gas and many other things that would be the most practical more that specific scenario. As mentioned on pubmed, hospital administrators have a limited amount of money that they can spend on medicine and other health services(pubmed1). They also have to balance the hours spent in operating rooms and who is spending them, and they figure out the most convenient, cheapest, or all around best way to distribute all of these variables by using linear programming(pubmed1). On Chron.com they use the following steps to show how restaraunts can ue linear programming:
Restaurants use linear programming for menu planning. It uses basic algebra to optimize meal production and thereby increase restaurant profits. Linear algebra reflects a direct relationship between an increase or decrease in food resources, and an increase or decrease in meal production. For example, if the kitchen has only half its needed supply of cream base, then it can only prepare half its normal amount of cream soups. Additionally, management can determine the cost of preparing different menu items to decide how many of each menu item to prepare for optimal profit.
Step 1
Choose the decision variables that apply. In this example, a restaurant needs to produce 250 of its dinner specials per day, one with meat and the other vegetarian. The decision variables are the number of meals and the different menu names (i.e., porterhouse steak and spinach lasagna).
Step 2
Choose the objective for the restaurant. Normally, the objective is to determine how many of each menu item to prepare that meets the required number of meals yet stays within budget, so this is the objective for the example shown. However, the objective will be the quantity of physical supplies on hand, if there is a shortage of a particular ingredient that several menu items use, such as tomato sauce. Then management can determine how to get the largest number of meals with the quantity of tomato sauce on hand.
Related Reading: Restaurant Menu Writing Guidelines
Step 3
Choose the constraints on menu production, which is the day’s monetary budget to produce a specified number of meals. For example, a restaurant has a $1,000 budget for that day’s two dinner specials, and it must prepare 250 meals that cost different amounts to prepare. It cannot spend more than $1,000 and still earn a profit.
Step 4
Choose the two dinner specials, such as porterhouse steak and spinach lasagna. For this example, the porterhouse steak costs $7 to prepare and the lasagna dinner costs $3. The steak is designated as “S” and the lasagna as “L."
Step 5
Calculate how many steak dinners the restaurant can prepare for $1,000: S + L = 250 meals. 7S <= $1,000 S <= $1,000 / 7 = 142.85 S = 142 meals for $1,000 (The restaurant cannot serve 85/100 of a meal, so that amount is dropped.)
Step 6
Calculate how many lasagna dinners the restaurant can prepare for $1,000. 3L <= $1,000 L <= $1,000 / 3 = 333.33 L = 333 meals for $1,000
Step 7
Calculate the ratio: 142S divided by 333L = 42 percent (drop the decimals). This means that 42 percent of the meals should be steak dinners. Conversely, 58 percent of the dinner specials should be spinach lasagna.
Step 8
Calculate the number of steak dinners the restaurant can prepare on its budget: 142S times 42 percent = 59 steak dinners (drop the decimals)
Step 9
Calculate the number of spinach lasagna dinners the restaurant can prepare on its budget: 333L times 58 percent = 193 lasagna dinners.
Step 10
Verify the quantity of meals: 59 steak dinners plus 193 lasagna dinners = 252 meals. Since the restaurant only has to prepare 250 meals, it is under budget, which means increased profit.
Step 11
Verify the cost: 59 steak dinners times $7 equals $413. 193 lasagna dinners times $3 equals $579. $413 + $579 = $992, which is under budget.(Perez1)
This is a prime example of how linear programming can be used to determine the best outcome or use of variables.
Paragraph: To use this concept, you need to be able to use basic operations such as addition, subtraction, multiplication, and division. You also need to know how to use variables. You also need to be able to graph linear equations, choose which variables will represent which interchangable factors, remember certain graphing equations and create them through real life scenarios. Last but not least, you need to decide what the best or most suitable option for your problem is.
Work Cited
Dexter F, Blake JT, Penning DH, Sloan B, Chung P, Lubarsky DA, Pubmed, 2002.
<http://www.ncbi.nlm.nih.gov> 6 March, 2014.
Diane Perez. Chron, 2014. <http://smallbusiness.chron.com> 12 March, 2014.
Merriam Webster. Britannica, 2014. <http://www.merriam-webster.com/> 3 March, 2014.
Purplemath. 2012. <http://www.purplemath.com> 4 March, 2014.
Stephanie Ellen. ehow, 2014. <http://www.ehow.com> 4 March, 2014.
For this project, we each chose a mathematical topic such as linear programming, radical functions, linear equations etc. After we were assigned them, we had to research the topic and find jobs that use it, the definition, the skills needed to be able to use it, and an example of how it is used. After we finished that, we had to make a presentation out of it such as a poster board, or slideshow.
Linear Programming by Max Jaye
Definition: According to Merriam-Webster, linear programming is, “a mathematical method of solving practical problems (as the allocation of resources) by means of linear functions where the variables involved are subject to constraints”(Merraim-Webster).
Refined definition: Linear programming is a way to project or decide outcomes of things by using restricted variables such as money, time, size, amount, etc.
Careers that use linear programming: Professions that use linear programming include being a dental assistant, doctor, pilot, business manager, or a zookeeper(ehow1). This concept can be used to estimate the amount of medicine, food, gas and many other things that would be the most practical more that specific scenario. As mentioned on pubmed, hospital administrators have a limited amount of money that they can spend on medicine and other health services(pubmed1). They also have to balance the hours spent in operating rooms and who is spending them, and they figure out the most convenient, cheapest, or all around best way to distribute all of these variables by using linear programming(pubmed1). On Chron.com they use the following steps to show how restaraunts can ue linear programming:
Restaurants use linear programming for menu planning. It uses basic algebra to optimize meal production and thereby increase restaurant profits. Linear algebra reflects a direct relationship between an increase or decrease in food resources, and an increase or decrease in meal production. For example, if the kitchen has only half its needed supply of cream base, then it can only prepare half its normal amount of cream soups. Additionally, management can determine the cost of preparing different menu items to decide how many of each menu item to prepare for optimal profit.
Step 1
Choose the decision variables that apply. In this example, a restaurant needs to produce 250 of its dinner specials per day, one with meat and the other vegetarian. The decision variables are the number of meals and the different menu names (i.e., porterhouse steak and spinach lasagna).
Step 2
Choose the objective for the restaurant. Normally, the objective is to determine how many of each menu item to prepare that meets the required number of meals yet stays within budget, so this is the objective for the example shown. However, the objective will be the quantity of physical supplies on hand, if there is a shortage of a particular ingredient that several menu items use, such as tomato sauce. Then management can determine how to get the largest number of meals with the quantity of tomato sauce on hand.
Related Reading: Restaurant Menu Writing Guidelines
Step 3
Choose the constraints on menu production, which is the day’s monetary budget to produce a specified number of meals. For example, a restaurant has a $1,000 budget for that day’s two dinner specials, and it must prepare 250 meals that cost different amounts to prepare. It cannot spend more than $1,000 and still earn a profit.
Step 4
Choose the two dinner specials, such as porterhouse steak and spinach lasagna. For this example, the porterhouse steak costs $7 to prepare and the lasagna dinner costs $3. The steak is designated as “S” and the lasagna as “L."
Step 5
Calculate how many steak dinners the restaurant can prepare for $1,000: S + L = 250 meals. 7S <= $1,000 S <= $1,000 / 7 = 142.85 S = 142 meals for $1,000 (The restaurant cannot serve 85/100 of a meal, so that amount is dropped.)
Step 6
Calculate how many lasagna dinners the restaurant can prepare for $1,000. 3L <= $1,000 L <= $1,000 / 3 = 333.33 L = 333 meals for $1,000
Step 7
Calculate the ratio: 142S divided by 333L = 42 percent (drop the decimals). This means that 42 percent of the meals should be steak dinners. Conversely, 58 percent of the dinner specials should be spinach lasagna.
Step 8
Calculate the number of steak dinners the restaurant can prepare on its budget: 142S times 42 percent = 59 steak dinners (drop the decimals)
Step 9
Calculate the number of spinach lasagna dinners the restaurant can prepare on its budget: 333L times 58 percent = 193 lasagna dinners.
Step 10
Verify the quantity of meals: 59 steak dinners plus 193 lasagna dinners = 252 meals. Since the restaurant only has to prepare 250 meals, it is under budget, which means increased profit.
Step 11
Verify the cost: 59 steak dinners times $7 equals $413. 193 lasagna dinners times $3 equals $579. $413 + $579 = $992, which is under budget.(Perez1)
This is a prime example of how linear programming can be used to determine the best outcome or use of variables.
Paragraph: To use this concept, you need to be able to use basic operations such as addition, subtraction, multiplication, and division. You also need to know how to use variables. You also need to be able to graph linear equations, choose which variables will represent which interchangable factors, remember certain graphing equations and create them through real life scenarios. Last but not least, you need to decide what the best or most suitable option for your problem is.
Work Cited
Dexter F, Blake JT, Penning DH, Sloan B, Chung P, Lubarsky DA, Pubmed, 2002.
<http://www.ncbi.nlm.nih.gov> 6 March, 2014.
Diane Perez. Chron, 2014. <http://smallbusiness.chron.com> 12 March, 2014.
Merriam Webster. Britannica, 2014. <http://www.merriam-webster.com/> 3 March, 2014.
Purplemath. 2012. <http://www.purplemath.com> 4 March, 2014.
Stephanie Ellen. ehow, 2014. <http://www.ehow.com> 4 March, 2014.
Reflection
I think that this project was mapped out in a very organized way and was very relevant to the real world. Although, my favorite part of the project was how we all got different topics which made it less boring and repetitive. My least favorite part of this project was researching, mostly because I am bad at it, but also because it doesn’t excite me very much. If I could do this project again, I would take my time and focus less on the requirements, and just try to make the absolute best work that I can.
I think that this project was mapped out in a very organized way and was very relevant to the real world. Although, my favorite part of the project was how we all got different topics which made it less boring and repetitive. My least favorite part of this project was researching, mostly because I am bad at it, but also because it doesn’t excite me very much. If I could do this project again, I would take my time and focus less on the requirements, and just try to make the absolute best work that I can.
The piece of work that I am the most proud of in Math this year is definitely my landscape project. I think that it is so good because I didn’t rush through it. I knew I could finish it in time and I just wanted to get a good grade on it. one of the reasons that I like it so much is because of how neat it is. There are no overlapping lines or smears. Another reason that I like it is because of how realistic it is. Not only does it look realistic but it actually is taken from a real picture of the New York skyline. Through this mini-project, I learned how to graph all six types of lines and I also learned how much better I work when I take my time.