Question

The manufacturer of a CD player has found that the revenue R (in dollars) is R(p)= -4p2+1200p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar? (Find the Vertex)

Answer 1

Answer: 9000$

Step-by-step explanation:

Let 's use the formula to find the vertex of the parabola:

ax²+bx+c=0

$\displaystyle x_v=-\frac{b}{2a} \\\\ Where :\\\\ y_v- maximum \ \ income \\\\ y_v=a(x_v)^2+bx_v+c \\\\ Then \ in \ \ our \ \ case : \\\\ -4p^2+1200p =0 \\\\ x_v=-\frac{1200}{-4\cdot 2} =150 \\\\ y_v=-4\cdot (150)^2+150\cdot 1200 \\\\ y_v=150\cdot 1200-150\cdot 600 \\\\ y_v=600\cdot 150=\bf 9000$