StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...
Free

Real World Quadratic Functions - Essay Example

Cite this document
Summary
They find wide application in forecasting profits and losses in business and assisting in the determination of maximum and minimum values (Harshberger & Reynolds, 2013). A…
Download full paper File format: .doc, available for editing
GRAB THE BEST PAPER96.6% of users find it useful
Real World Quadratic Functions
Read Text Preview

Extract of sample "Real World Quadratic Functions"

Real World Quadratic Functions Introduction Quadratic functions have wide application in not only science and engineering but also in business. They find wide application in forecasting profits and losses in business and assisting in the determination of maximum and minimum values (Harshberger & Reynolds, 2013). A quadratic function is one that takes the form of f(x) = ax2 + bx + c. In this assignment, the daily profit recorded in the chain store would be determined by the number of clerks employed.

The maximum profit would be determined from the profit function, P(x) = -25x2 + 300x, where:P – daily profit,x – number of clerksP = -25x2 + 300xThe x-intercepts would be deduced from solving -25x2 + 300x = 0. Multiplying through by -1;25x2 - 300x = 0 Factoring the left hand side;25x(x - 12) = 0 Using the Zero Factor Property;25x = 0 or x - 12 = 0 Solving both equations;x = 0 or x = 12 An indication of a parabola intersecting with the x-axis at 0 and 12.The maximum value for the graph would occur where b = 300 and a = -25; c = 0.

Borrowing from Harshberger and Reynolds (2013), with a > 0, the parabola would open upwards as opposed to when a < 0 where it would open downwards. Since in this case a = -25 < 0, the parabola opens downwards with the maximum value of P being found at the vertex of the parabola.To determine the number of clerks that would maximize profits, the x-coordinate of the vertex would be employed given by:x = -b/2a = -300/2(-25) = 6Therefore, with 6 working clerks would be needed for the profits would be maximized.

To determine the maximum possible profits;P(6) = -25(6)2 + 300(6)P(6) = -25(36) + 1800P(6) = -900 + 1800Thus, a possible maximum profit of 900 would be expected with 6 clerks working.It would be deduced from this graph that with no clerks working, there would no profits made just as there would be no profits made with the engagement of 12 clerks. Maximum profit would be achieved with 6 clerks working. This function gives a graph whose relevance only holds in the first quadrant.Importance to managersQuadratic functions play a critical role in business cases with managers using these functions to determine the amount of workforce or units needed to obtain the greatest possible profit returns (Harshberger & Reynolds, 2013).

Similarly, they help in forecasting the expected profits or losses hence assist in planning. These functions vary from one company to another thus the importance of each manager to determine the function that truly reflects the operations of the managed firm. ConclusionQuadratic functions would be applied in various real world situations to find meaningful solutions. In this assignment, its usefulness in determining the maximum profit and how to maximize profits in a business entity has been illustrated.

From this, it would be noted that solving a quadratic function problem requires the determination of vertex or description of the parabola’s section.ReferenceHarshbarger, R. J. & Reynolds, J. J. (2013). Mathematical applications for the management, life, and social sciences (10th ed.). Boston, MA: Brooks/Cole.

Read More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Real World Quadratic Functions Essay Example | Topics and Well Written Essays - 500 words”, n.d.)
Retrieved from https://studentshare.org/mathematics/1612672-real-world-quadratic-functions
(Real World Quadratic Functions Essay Example | Topics and Well Written Essays - 500 Words)
https://studentshare.org/mathematics/1612672-real-world-quadratic-functions.
“Real World Quadratic Functions Essay Example | Topics and Well Written Essays - 500 Words”, n.d. https://studentshare.org/mathematics/1612672-real-world-quadratic-functions.
  • Cited: 0 times

CHECK THESE SAMPLES OF Real World Quadratic Functions

Model Predictive Control

quadratic program at each sampling time.... The detection and diagnosis of abnormal conditions in industrial plants is important for several reasons that include reducing variability in product quality, detecting equipment wear or instrument malfunction, and ensuring plant safety....
18 Pages (4500 words) Essay

TD LOG501 case 3

This employment of optimization will ensure there is no shortage or surplus which may have occurred had the functions been managed separately.... We also have the quadratic optimization, which entails all the LP programs, and more applications in scheduling, planning and computations hence aid in solving many other problems....
1 Pages (250 words) Essay

Linear Model and Nonlinear Model

This is the common case by which the line of best fit is determined in this scenario.... Regression, in this context, refers to the process by which an… When plotting for a regression line in the scatter plot, one needs to be careful on how to deal with the outlier values which may not feature anywhere around the regression line (Vonesh 75)....
8 Pages (2000 words) Essay

Real World Quadratic Functions

The daily profit, P of a chain store is Real World Quadratic Functions MAT 222 Week 4 Assignment Real World Quadratic Functions A quadratic function has theform , where, a, b and c are real numbers with a ≠ 0.... For solving a quadratic function, rules for order of operations, solving equations, exponents, and radicals are used.... The graph of a quadratic function is given by a parabola that opens either… When the parabola opens downward, the vertex is the point where the relative minimum of the function occurs and when the parabola opens upward, the vertex is the point where the relative maximum of the function occurs....
2 Pages (500 words) Coursework

Quadratic equations

In the real world, ‘Quadratic Equations' can prove useful in a number of ways as –(1) Modeling costs for a general store –In C(x) = -0.... The cost may be predicted to decline once the store decides to purchase materials greater than this value of ‘x' on Can you think of examples of processes that could be modeled with quadratic equations?... Physicists characterize this scenario in a kinematic equation that is quadratic by nature, being y = V0y*t - ½ gt2 in which ‘y' represents displacement of the ball whereas V0y is the initial velocity, along the vertical....
1 Pages (250 words) Assignment

The Nature of Mathematical Modeling

This paper explains what models are and attempt a few problems to show how they are used to solve problems in the real world.... In this report, the principles of mathematical modelling are used to solve problems in the real world.... The models, create an image that makes the person carrying out the analysis to think critically and come up with a possible solution,… Models have been in use for a long period....
3 Pages (750 words) Essay

Maria Gaetana Agnesi

The values are derived if derivative of the cubic function is equal to zero which results to an equation that utilises the quadratic formula to obtain the values of x.... The world of Maria Gaetana Agnesi, Mathematician of God.... If f(x)=0 a cubic equation is in production of the form where x3 is x is in the power of 3 X2 is x in the power of 2 The coefficients a,b,c and d represent real numbers, in addittion, when solving the cubic functyion, it mainly refers to finding the specific value of x assuming that f(x)=0....
2 Pages (500 words) Research Paper

Speech Recognition and Speaker Recognition

The author of this coursework "Speech Recognition and Speaker Recognition" describes some methods and techniques which are used in the speaker recognition and speech recognition systems so as to enhance the security as well as provide good outcomes.... nbsp;… It can be applied to make out the identity of a person....
6 Pages (1500 words) Coursework
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Contact Us