Real World Quadratic FunctionsProblem #56 Maximum profit. A chain store manager has been told by the...

Question

Real World Quadratic FunctionsProblem #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?The assignment MUST contain the 2 steps below:	Solve problem 56.	Write a two to three page paper that IS VERY SIMILAR to the PDF example attached, 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 the attached PDF example.			Document Preview:				Real World Quadratic Functions Problem #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 = -25x2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit? The assignment MUST contain the 2 steps below: Solve problem 56. Write a two to three page paper that IS VERY SIMILAR to the PDF example attached, 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 the attached PDF example.

David · Accepted Answer

Sol: Profit function 
2
P(x)=-25x300x,
+
 where x is the number of clerks working.
  This equation is similar to the equation of parabola 
2
,
yaxbxc
=++
             Where 
25, 300, and 0,
abc
=-==
 The x-intercepts of the parabola can be found by solving 
2
-25x300x=0.
+
               
(
)
2
-25x300x=0           Divide both sides b
y -1.
2
25x-300x=0               Factor the left
 side.
25xx-120              Use Zero Factor Pr
operty.
25x=0  or  x-12=0        Solve each equa
tion.
x=0  or x=12 
+
=
               The parabola will cross t
he x-axis at 0 and 12.
This quadratic function has a large 
a
 value which means the parabola will be narrow. It also has a negative 
a
value so the parabola will open downward. This means there will be maximum value of the graph at the vertex which will happen at the x value of 
,
2
b
a
-
 where 
300 and 25
ba
==-
in this case.
What number of clerks will maximize the profit?
     
(
)
300150
6             6 clerks working will maxi
mize 
2
22525
                                        
               profit.
b
a
-
-
===
-
What is the maximum possible profit when this many clerks are working?

Real World Quadratic Functions Problem #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 ,...

Answer To: Real World Quadratic Functions Problem #56 Maximum profit. A chain store manager has been told by...

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment