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Mathematics

Cost Function

  1. Regrind, Inc. reginds used typewriter platens. The cost to buy back each used platen is $2.60. The fixed cost to run the grinding machine is $195 per day. If the company sells the regroundplatens for $7.60, write a cost function, a revenue function, and determine how many platens must be reground daily to break even? (Assume that there are no unsold platens at the end of the day.)
    (a) Express the Cost C as a function of x.
    C(x)=
    (b) Express the Revenue as a function of x.
    R(x)=
    (c) Determine analytically the value of x which revenue equals cost.

(a)

Where x represents the number of days and p represents each individual platen, the cost is represented as follows:

C(x) = $195x + $2.60p

(b)

Where x represents the number of days and p represents each individual platen, the revenue is represented as follows:

Categories
Mathematics

Question 10 and 12

Given the data, the cost duration history is: $0 for the first two days- $15 for the second day and $90 for the third day.

The least cost schedule for the planned activities are:

  • 1-2 Contract Personnel- $180 dollars
  • 2-3 Obtain stage props-  $120 dollars
  • 3-4 Rent equipment – $160 dollars
Categories
Mathematics

Performance Assessment

 

Introduction

Performance monitoring is very important for the project to determine whether the expected developments are achievable. Performance monitoring is very important to understand the elements of costs, technical issues and schedule processes for the project. This compared against the baseline of the project inculcates the issues of Planned Value, Earned Value and the Actual cost incurred in the project. Monitoring the performance of the project is cardinal to ensure that the level of performance at each stage matches with the value baseline. Performance management is important to ensure that all the objectives of the project are achieved. The approach enables the organization to determine the future performance and changes in the project lifecycle. The earned baseline provides a suitable stance for comparing the actual performance of the project and the targeted performance. It acts as the benchmark for comparing the current data with the past figures and develop a analysis which can be used asses the performance of the project. The comparison adopted in this study will rely on past data and the current data to ensure a concise and clear comparison. The past data was developed by adhering to proper practices that entailed the project scope, resource estimating techniques, budgets, the earned value calculations, fiduciary responsibility, and the effects of Sarbanes-Oxley compliance, to ensure that information deduced for the project were reliable and enhanced transparency and accountability to the management of the organization and to the shareholders of the company (Alfieri, et al, 2011).

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Mathematics

Saving for Retirement

Retirement Analysis:

I am currently 30 years old; I hope to retire at the age of 50 years old.  Thus, I have 20 years until I plan to retire.

I estimate that after I retire at the age of 50, I will need to draw roughly $20,000 from savings per year.  I currently participate in a defined contribution plan through a 401 k.

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Mathematics

Percents and Earning Interest

Scenario #1

Last season, a pair of jeans cost $44.95. This season, the price of all jeans increased by 15 percent. Later in the season, the jeans were put on sale for 15 percent off.

  • How much did the jeans cost at the beginning of the season?
  • What was their sales price?
  • Were you surprised by the sale price of the jeans? Why or why not?
Categories
Mathematics

Math Problem: Pool

The problem was given in units of feet and inches.  The units were all converted to metric units in order to obtain the cubic volume measurements.  The width of the pool was converted from 16.4 feet wide to 5.00 m wide.  The length of the pool was converted from 26.25 feet long to 8.00 m long and the depth was converted from 5 feet deep to 1.52 m deep.  In addition, the loss of water from evaporation was converted from 10 inches to 0.254 m.  Furthermore, the average rate of water flow in Jill’s garden hose was converted from 10 gallons/minute to 37.85L/minutes, which was further converted to cubic meters at 0.0379cm3.   The second part of the problem was to find out how many liters of water Jill would need in order to fill her pool to the original depth from evaporation loss.  In order to find the solution, the original volume of the pool was calculated at 60.8 cm3 using the Volume formula (l x w x h).   The original depth of 1.52 m was then subtracted from the water loss of 0.254 m and the new volume of the pool was calculated to be 50.8cm3.  The original volume (60.8cm3) and the new volume of the pool (50.8cm3) were subtracted to obtain the amount water in liters and gallons needed to fill the pool.  The amount of water that Jill needs in order to fill the pool was 10,000 Liters or 2641 gallons of water.  Finally, the amount of time needed to fill the pool with 2641 gallons of water was calculated.  If Jill’s hose could pump 10 gallons of water per minute, the amount of time needed is 264.1 minutes.

Categories
Mathematics

Net Promoter Makes Our Business

The net promoter score is one that makes or breaks a business. Many consumers are able to see the net promoter scores for businesses. This customer service oriented score defines the satisfaction of customers for many different types of businesses. According to Wikipedia (2013), the “net promoter is a management tool that can be used to gauge the loyalty of a firm’s customer relationships. It serves as an alternative to traditional customer satisfaction research.” These scores are not only helpful to consumers, but also helpful to the businesses that use them as they explain how satisfied the company is making its customers. The net promoter score can be as low as -100 or as high as +100. Anything that is positive is said to be good, but anything over +50 is said to be excellent when using this tool (Wikipedia, 2013). The article entitled “Measuring your Net Promoter Score” (2013) states the following:

Categories
Mathematics

Applications of Graph Theory

Abstract

Graph theory is the study of graphs which shows a relational impact between different areas, functions, entities or other catalysts. The graph is a model representation of the relationships or processes and provides a practical representation of dynamic information. Specifically in the representation of networks the graphs can represent communication models, data organization, information flow and computations and logic relationships. The application of graph theory spans multiple areas of study such as mathematics, biology, sociology and computer sciences. One key area for utilization of graph theory is in the development of a knowledge management system and the development of how that knowledge is transferred across networks. The development of those networks takes resources to plan, configure, implement, monitor and control. Assigning these resources requires tools to ensure effectiveness and efficiency are established. Within computer science networking is increasing in importance due to the exponential growth in demand for connectivity and the need for efficiency and security of those networks. There are many examples of utilizing graph theory in computer networks such as providing the framework for optimization of the network in terms of connectivity, reliability and efficiency.

Areas of Application Overview

Within computer science there are many areas that benefit from the implementation of the graph theory. By showing relationships, defining dependencies and allowing a representation of the effectiveness and the opportunity for optimization, the graph theory provides a tool for ensuring security, determining data flow, processing data into information and planning network paths and allocating resources. The areas of focus for the practical application of graph theory include knowledge management systems which require interrelated networks of data and the security of that data specifically focused on wireless networks.

Knowledge Management System Development

There are many challenges when developing a knowledge management system. When developing or implementing any new idea or project there are hurdles that the project team will encounter that span outside of the viability and functionality that the project is going to provide There are outside factors that could present themselves as obstacles but understanding those challenges can turn those obstacles into opportunities. These challenges include factors such as the culture of the people providing the knowledge as well as those accepting the knowledge, value of the knowledge, the orchestration and preparation of the knowledge for consumption and use as well as the integration and flow of knowledge for full implementation for the end users.

To understand the challenges of the knowledge management system life cycle it is first critical to understand what knowledge management is and what encapsulates its lifecycle. The knowledge management’s purpose is to package knowledge from subject matter experts regarding key systems, processes, procedures, experiences or insights and provide that knowledge to others within the organization (Hislop 2009).

There are three key areas that provide a basis for the knowledge that is in the knowledge management system. These three areas provide a challenge due to the fact that if any are neglected the system would become antiquated and unusable. These areas are data accuracy, interpretation and relevancy (Becerra-Fernandez, Sabherwal, and Gibson). The first is data accuracy which means that the knowledge or data that is inputted into the system must be accurate and ultimately reliable. The challenge is ensuring the accuracy and maintaining the level of effort required for validation of the data. The next is the ability for the information to be interpreted by the user. The data that is inputted into the knowledge management system must be able to be meaningful and usable to the end user. Without usable information the system will fail. Lastly of the three, the relevance is critical. This falls in line with obsolete information and the power of the data relies on how up-to-date the data is and how it relates to the knowledge required by the end user. Managing these three areas is a challenge to the knowledge management system because without a focus on all three of these areas the system would not be utilized to its intended purpose.

Networking in Computer Science-Data Security

With the ever increasing reliance on wireless networks there are more opportunities for risks to data by external forces trying to take advantage of the security weaknesses of a wireless network. There are many threats to wireless networks and many of these risks can cause damage to the organization’s and customers’ data. The first type of attack would include gaining access by going right into the network. Without the proper security measures an intruder could gain access to the wireless network by sniffing out the wireless signal and logging into the system which grants access to key data and business information. These types of attacks can be active or passive. The active attack is where the intruder is actively seeking out ways to intrude into the network and there is also passive ways for malicious entities to hinder a network. The active risks include direct access to an authorized network access, network hijacking, denial of service and flooding the network with unnecessary requests which limits the ability for the network to be used (Hayden, 2010). The passive attacks utilizes software programs to seek out unsecured or weakly secured networks and accesses them through the program to gain access and cause a disruption. These attacks can be limited and reduced with the appropriate network security measures such as password protection, encryption and other software and hardware security measures. Through the use of the graph theory key security areas are identified and can easily have resources assigned to address the potential security issues. This documentation allows the graphical representation of the security network to become more of a security tool than a diagram of security points in the network.

Graph Theory

Graph theory is used to represent in a graphical representation a group of relational items. The purpose of this graphical representation is to show a direct correlation between items and how they link together. This is important in the application of graph theory in the computer science field of study specifically in the area of networks and how the network sends and receives data from one point to the next. The graphs are used to model not only the relationships between the processes and data flow but also the dynamic effects each point in the process has upon the preceding and future points in the process. There are two areas that are specific to graph theory that provide assistance in developing the area of networks in the field of computer science. These areas are flow network and Max-flow min-Cut theorem. These are focused on key areas of a network in regard to flow and capacity as well as efficiency and optimization.

The flow network is a directed graph, a graph that has a specific direction associated to it, that has a specific capacity or capability in which each edge of the graph can operate (van Steen, 2010). This capacity defines limits in which the flow can operate and provides not only a visual awareness to areas that can be monitored and controlled to adjust the network to function properly but also ensure that resources are properly allocated to maintain the appropriate level of capacity at each edge. In networking the flow diagram would allow the insight into data flow from one area to another and would determine areas that are exceeding capacity or other areas that have too many resources allocated and provides more capacity than required by the system.

The Max-flow min-Cut theorem is an optimization function of the graph theory that represents the max flow of a system or network (van Steen, 2010). This show the total amount of data, in the case of a knowledge management network, that can be processed at any given time. This type of information would also provide the key inputs into how a network can be optimized or integrated into an overall security plan to ensure efficiency, effectiveness, security and reliability of the system is optimized.

The overall purpose of the graph theory is not to provide every facet of network development or ensure every security measure is taken but to provide a tool to raise the awareness of key points of opportunity and avoid those key points of failure that would not normally have the awareness without the graphical representation allotted by the graph theory’s use.

Graph theory has advanced the knowledge and understanding in both development of the knowledge management systems and network security by allowing contextual visualization on key points within each of the systems as a whole. The implementation of a knowledge management system requires an infrastructure built on a network designed to perform to a specific set of parameters while avoiding information choke points and restrictions that are caused by specific areas in the network. These areas can be determined through the max-flow min-cut theorem to show where additional capacity should be accomplished or where resources providing capacity that is not require could be reallocated to level out the total capacity of the system to allow adequate data flow.

Conclusion

Graph theory’s application has practical use in the development of secured networks and the capacity management of knowledge management systems that base their utilization on the networks in which they are housed. The foundation of a secure system and an effective and efficient network is enhanced through the use of flow network and Max-flow min-Cut theorem. These areas allow the continual improvement of the network to right-size the limited resources based on the outputs of the graph theory.  Capacity management, resource utilization, maximum flow and security optimization are all benefits of the graph theory.

 

References

Becerra-Fernandez, I., R. Sabherwal, and C. F. Gibson. (2010). Knowledge management : Systems and processes. Armonk: Sharpe Incorporated. Print

Hayden, L. (2010). It security metrics. New York: McGraw Hill.

Hislop, D. (2009). Knowledge management in organizations: A critical introduction. 2nd. New York : Oxford University Press. Print

van Steen, M. (2010). Graph theory and complex networks: an introduction. Amsterdam: Maarten van Steen. Retrieved from http://www.distributed-systems.net/index.php?id=graph-theory-and-complex-networks

Categories
Mathematics

Estimation: A Real Life Mathematical Tool

Estimation in mathematics is a process of approximation where the value is uncertain, or unstable; however estimation does involve statistical formulas derived from a sample to help approximate the final value. Although estimates aren’t certain numbers, they are the best approximation a person can make in an event where the variable they are working with are unstable or changing.

Categories
Mathematics

Solution to Megan’s concern

Megan Bedding, vice-president of sales for International Microcircuits, Inc. (IM), was delighted when IM was one of the few firms invited to enter a bid to supply a large industrial customer with their major product in a small foreign country. However, her top salesperson for that region had just called and informed her of certain “expectations” of doing business in the country:

1. Local materials at least 50 percent of the products value must be purchased in reciprocity.

2. The local politicians will expect continual significant donations to their party.

3. Industrial customers normally receive a 40% “rebate” (kick back) when they purchase goods from suppliers such as IM. (IM’s profit margin is only 20%.)

With this new information, Megan was unsure about changing or proceeding with the bid. If it was withdrawn, a lot of effort would be wasted as well as a chance to get a foothold in the international market. But if she proceeded, how could these expectations be met in a legal and ethical way?

Categories
Mathematics

History of algebra

Introduction

This paper explores the history of algebra; it will deeply describe how the algebra started and who were the core founders and facilitators of algebra movement to different parts of the continent. It will indicate how the algebra started and how it has worked in science and mathematics in different countries and its use in the current world. Therefore, algebra is a branch of mathematics which uses symbols mostly than definite numbers for mathematical arithmetic operations. This form of mathematics is divided into three branches; linear algebra, elementary, and modern algebra. The history of algebra can be traced all the way from Egypt and Babylon, from this places people could easily solve equations such as linear (ax=b) and also quadratic equations such as ax+bx=c. People from Babylon could easily solve quadratic equations with the current method taught in schools nowadays. It is argued that the father or founder of algebra was the Alexandrian Greek mathematician known as Diophantus in between 200AD-284AD, which later became the tradition of Egyptians and Babylonians through Diophantus. Also there has been a debate among different people that the al-Khwarizmi the Arabian mathematician who wrote the book of Al-jabr also known as ‘’ the ‘’science of restoration’’ is the founder of the algebra and deserves the title while others have argued that the Diophantus who wrote the book of arithmetica is the father of the algebra (NovZ, 2004).

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Mathematics

The Life and Times of Leonhard Euler

Once, or maybe twice, every century there comes a mind that was seemingly methodically placed on this plane, with the simple purpose of reinventing the way the entire world sees even trivial, everyday occurrences. Sometimes this thinker is a philosopher, as in someone like Henry David Throeau–very often however, with specific examples of Roman and Greek thinkers, this person comes from the mathematics or science discipline. This is certainly the case with brilliant 18th century mathematician Leonhard Euler, who arguably contributed more to modern mathematics than anyone else in history.

Born in Basel, Switzerland on April 15, 1707, Leonhard Euler was born the son of a Calvinist pastor, and originally studied theology and Hebrew himself. Attending the University of Basel, his life’s plan was originally to follow his father into a member of the Church. In 1724, he graduated from the institution, where he had been “privately tutored” by the world renowned mathematician John Bernoulli. In fact, it was this man himself that single-handedly convinced Euler’s father to allow Euler to pursue mathematics as a career, a testament to the brilliance of even the early mind of Leonhard Euler (Golba, 2007).

Categories
Mathematics

Statistics Data Regression/ Slope Analysis

1) For the first set of data a regression analysis (easiest to copy and paste into statcrunch).

  1. a) Find the correlation coefficient r.

.137

Categories
Mathematics

Home Market Value

House Age Square Feet Market Value
33 1 812 $90 000,00
32 1 914 $104 400,00
32 1 842 $93 300,00
33 1 812 $91 000,00
32 1 836 $101 900,00
33 2 028 $108 500,00
32 1 732 $87 600,00
33 1 850 $96 000,00
32 1 791 $89 200,00
33 1 666 $88 400,00
32 1 852 $100 800,00
32 1 620 $96 700,00
32 1 692 $87 500,00
32 2 372 $114 000,00
32 2 372 $113 200,00
33 1 666 $87 500,00
32 2 123 $116 100,00
32 1 620 $94 700,00
32 1 731 $86 400,00
32 1 666 $87 100,00
28 1 520 $83 400,00
27 1 484 $79 800,00
28 1 588 $81 500,00
28 1 598 $87 100,00
28 1 484 $82 600,00
28 1 484 $78 800,00
28 1 520 $87 600,00
27 1 701 $94 200,00
28 1 484 $82 000,00
28 1 468 $88 100,00
28 1 520 $88 100,00
27 1 520 $88 600,00
27 1 484 $76 600,00
28 1 520 $84 400,00
27 1 668 $90 900,00
28 1 588 $81 000,00
28 1 784 $91 300,00
27 1 484 $81 300,00
27 1 520 $100 700,00
28 1 520 $87 200,00
27 1 684 $96 700,00
27 1 581 $120 700,00