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# Real World Quadratic Functions (Math Problem Sample)

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Read the following instructions in order to complete this assignment:
Solve problem 56 on pages 666-667 of Elementary and Intermediate Algebra.
56)Maximum profit. A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P = −25x^2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?
Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include:
An explanation of the basic shape and location of the graph and what it tells us about the Profit function.
Your solutions (it is a double question) to the above problem, making sure to include all mathematical work for both problems.
Discuss how and why this is important for managers to know, and explain what could happen if the ideal conditions were not met.
The paper must be at least two pages in length and formatted according to APA style
source..

Content:

Real world quadratic equation
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Profit = P,
Number of clerks = x,
Function relating profit to number of clerks; P = âˆ’25x^2 + 300x,
The above function is a quadratic function relating the two variable P and x.
In order to find the maximum profit first is to finding the value of the axis of symmetry given as:
X = -b/2a,
Where from the function P = âˆ’25x^2 + 300x,
a = -25 and b = 300.
Therefore substituting the values of a and b,
X = -300/ 2* (-25),
X = -300/ -50,
X = 6, The negative coefficients cancel out after dividing.
This means that a maximum of 6 clerks will be required in order to maximize the profit.
From the function P = âˆ’25x^2 + 300x, in order to find the maximum profit replace x with the true value of clerks which is 6.
P = -25 *6 ^ 2 + 300 * 6,
P = - 25 * 36 + 1800,
P = -900 + 1800,
Thus the profit is 900.
This is represented in the graph below:
The above curve shows the profit margin in relation to the number of clerks working in a given day. The profit rises with the increase of the number of clerks working up to a maximum of six clerks. The apex of the curve is the point whereby the company maximizes its profit. At this point no more than six clerks are required in ...

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