Question 881317
the solutions i came up with are:
x = 71.335 and x = 8728.6642
this was solved using the quadratic equation and also solved through graphing.


the equations that applied are:
p = 132 - .015x
that's your price equation.
r = px
that's your revenue equation.


you can substitute 132 - .015x for p in the revenue equation to get:


r = x * (132 - .015x)


simplify that to get:


r = 132x - .015x^2


you can graph that equation by substituting y for r.


the equation to graph is:


y = 132x - .015x^2


you can also graph the revenue equation of r = 9340 by graphing:


y = 9340


the intersection of these 2 equations on the graph will give you the values of x that will yield a revenue of 9340.


that graph is shown below:


<img src = "http://theo.x10hosting.com/2014/jun1103.jpg" alt="picture not found" </a>


in order to solve this equation using the quadratic formula, you had to set y = 9340 in the original equation of y = 132x - .015x^2 to get:
9340 = 132x - .015x^2
subtract 9340 from both sides of this equation to get:
0 = 132x - .015x^2 - 9340 which can also be shown as:
-.015x^2 + 132x - 9340 = 0


that equation is now in standard form and you get:
a = -.015
b = 132
c = -9340


now you can apply the quadratic formula of:
<pre>

               x = -b +/- sqrt(b^2 - 4ac)
                   ----------------------
                            2a
</pre>


the result of those calculations will get you:


x = 71.3358 or x = 8728.66


the value of x = 4400 is the value of the axis of symmetry which leads to the maximum point on the graph when you replace x in the original equation with 4400.


that would be the equation of y = 132x - .015x^2 which becomes y = 132(4400) - .015(4400)^2.


the result of that evaluation leads to the maximum point on the graph of 290400.