Problema Solution
The manufacturer of a CD player had found that the revenue R (in dollars) is R(x)=-4x^2+1280x when the unit price is x dollars. If the manufacturer sets the price to x to maximize revenue, what is the maximum revenue to the nearest whole dollar?
Answer provided by our tutors
we need to find the maximum of the function R(x)=-4x^2+1280x
R(x)=-4x^2+1280x
the quotient in front on x^2 is -4<0 thus the quadratic function has maximum in its vertex equal to c - b^2/4a where a = -5, b= 1280 and c= 0
R max = 0 - 1280^2/(4*(-4))
R max = $102,400.00
click here to see the graph of the function
the maximum revenue is $102,400.