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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)p(2,400 - 30p), where pp is the price per set in dollars. This expression can be written in factored form as −30p(p−80)-30p(p - 80).\newlineWhat does the number 8080 represent in the expression?\newlineChoices:\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)p(2,400 - 30p), where pp is the price per set in dollars. This expression can be written in factored form as −30p(p−80)-30p(p - 80).\newlineWhat does the number 8080 represent in the expression?\newlineChoices:\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
  1. Roots of Revenue Function: The root p=0p = 0 is obvious, as if the price is $0\$0, the revenue will be $0\$0. The other root is p=80p = 80. This means that if the price per set is $80\$80, the revenue will also be $0\$0.
  2. 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+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.
  3. Price Maximizing Revenue: In the expression −30p(p−80)-30p(p - 80), the value p=80p = 80 corresponds to the hh in the vertex form, which means it's the price that maximizes revenue.

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