Every year, the Gambo Toy Company releases a collector's set of miniature stuffed animals. The company has found that when it charges more per set, it sells fewer sets that year. Its revenue from selling the stuffed-animal sets, in dollars, can be modeled by the expression $p(2,400 - 30p)$ , where $p$ is the price per set in dollars. This expression can be written in factored form as $-30p(p - 80)$ . $\newline$ What does the number $80$ represent in the expression? $\newline$ Choices: $\newline$ (A)the price per stuffed-animal set in dollars so that Gambo's revenue is zero $\newline$ (B)Gambo's minimum revenue in dollars $\newline$ (C)Gambo's maximum revenue in dollars $\newline$ (D)the price per stuffed-animal set in dollars that maximizes Gambo's revenue

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Q. Every year, the Gambo Toy Company releases a collector's set of miniature stuffed animals. The company has found that when it charges more per set, it sells fewer sets that year. Its revenue from selling the stuffed-animal sets, in dollars, can be modeled by the expression

p(2,400 - 30p)

, where

p

is the price per set in dollars. This expression can be written in factored form as

-30p(p - 80)

\newline

What does the number

80

represent in the expression?

\newline

Choices:

\newline

(A)the price per stuffed-animal set in dollars so that Gambo's revenue is zero

\newline

(B)Gambo's minimum revenue in dollars

\newline

(C)Gambo's maximum revenue in dollars

\newline

(D)the price per stuffed-animal set in dollars that maximizes Gambo's revenue

Roots of Revenue Function: The root $p = 0$ is obvious, as if the price is $\$0$ , the revenue will be $\$0$ . The other root is $p = 80$ . This means that if the price per set is $\$80$ , the revenue will also be $\$0$ .
Maximum Revenue at Vertex: Since the revenue is modeled by a quadratic equation, the maximum revenue occurs at the vertex of the parabola. The vertex form of a quadratic equation is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Price Maximizing Revenue: In the expression $-30p(p - 80)$ , the value $p = 80$ corresponds to the $h$ in the vertex form, which means it's the price that maximizes revenue.