The demand equation for a certain product is given by p = 126 − 0.045 x , where p is the unit price (in dollars) of the product and x is the number of uni

Question

The demand equation for a certain product is given by
p
=
126
−
0.045
x
, 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
=
x
p
.

Determine prices
p
that would yield a revenue of 8330 dollars.

Lowest such price =

Highest such price =

Answer 1

R(x) = revenue if x is the unit price

 

R(x) = (price)(quantity) = (126 - 0.045x)(x)

 

                                   = -0.045x² + 126x

 

R(x) = 8300 when -0.045x² + 126x = 8300

 

                           -0.045x² + 126x - 8300 = 0

 

x = [-126 ± √14382] / (-0.09) = $67.50 or $2732.50