Quadratic word problem?! PRECALCULUS PLEASE HELP!??

Question

I have tried over and over again and I keep getting the wrong answer!
The demand equation for a certain product is given by p=122−0.035x , where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R=xp.

Determine prices p that would yield a revenue of 8310 dollars.

Lowest such price =
Highest such price =

 

 

I thought maybe since R=xp, R=x(122-0.035x)

 

R=122x - 0.035x^2

 

Then i dont know what to do. Thanks for the help!!

Answer 1

Hi Angelica,

 

 

   You are on the right track....

 

The demand equation for a certain product is given by p=122−0.035x , where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R=xp.

Determine prices p that would yield a revenue of 8310 dollars.

Lowest such price =
Highest such price =


I thought maybe since R=xp, R=x(122-0.035x)

R=122x - 0.035x²

 

The next step is the set the equation =8310

 

8310=122x-.035x²

 

-.035x²+122x-8310

 

Quadratic Formula

 

a=-.035

b=122

c=-8310

 

x=-122±√122²-4(-.035)(-8310)

    -------------------------------

                  2(-.035)

 

 

x=-122±√(14884-1163.4)

    -------------------------

            -.07

 

 

x=-122±√13720.6

    -----------------

            -.07

 

 

x=-122+√13720.6           and       x=-122-√13720.6 

     ----------------                           -----------------

             -.07                                              -.07

 

 

x=69.5005                     and        x=3416.2138

 

Since the x-values are prices round them to the hundredth place

 

x=69.50    and x=3416.21

 

ANSWER:  Prices p that would yield a revenue of 8310 dollars are p=$69.50 and p=$3416.21.

 

We're finished!