Problema Solution
The manufacture of the CD player has found that the revenue R (in dollars) is R(p)=-4p^2+1930p, when the unit price is p dollars if the manufactures sets the price p to maximize revenue, what is the maximum revenue to the nearest dollar?
Answer provided by our tutors
we need to find the maximum value of the function
R(p)=-4p^2+1930p
the function is parabolic with a quotient -4 < 0 in front of p^2 thus it has maximum
you can also notice that from graph of the function y = -4x^2 + 1930x
click here to see the graph
R max = c - b^2/(4a) where a = -4, b = 1920 and c = 0
R max = 0 - 1920^2/(4*(-4))
R max = $230,400
the maximum revenue is $230,400.