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The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by
R(p) = -25p2 + 1700p
where p is the price per unit (in dollars).
Find the unit price that will yield a maximum revenue.

Respuesta :

for a parabolic equation like R(p), the highest point is at the vertex, check the picture below

[tex]\bf \textit{vertex of a parabola}\\ \quad \\ \begin{array}{lccclll} R(p)=&-25p^2&+1700p&+0\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \textit{so the maximum revenue occurs when the price is }\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex]
Ver imagen jdoe0001

The value of unit price is $34

What is a parabola?

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

According to the given problem,

We know, in a parabolic curve, for maximum point,

[tex]\frac{d(R)}{dp}[/tex] = 0

⇒ [tex]\frac{d(-25p^{2}+1700p) }{dp}[/tex] = 0

⇒ -50p + 1700 = 0

⇒ 1700 = 50p

⇒ 50p = 1700

⇒ p = 1700/34

⇒ p = $34

Hence, we can conclude, the unit price for yielding the maximum revenue is $34

Learn more about parabola here: https://brainly.com/question/10572747

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