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Montox Timepieces manufactures and sells a special-edition wristwatch each year. The company has noted that when it charges more for each wristwatch, customers buy fewer of them that year. Its revenue from selling the wristwatches, in dollars, can be modeled by the expression p(1,080−6p)p(1,080 - 6p), where pp is the price per special-edition wristwatch in dollars. This expression can be written in factored form as −6p(p−180)-6p(p - 180).\newlineWhat does the number 180180 represent in the expression?\newline(A)Montox's maximum revenue in dollars\newline(B)Montox's minimum revenue in dollars\newline(C)the price per special-edition wristwatch in dollars that maximizes Montox's revenue\newline(D)the price per special-edition wristwatch in dollars so that Montox's revenue is zero\newline

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Q. Montox Timepieces manufactures and sells a special-edition wristwatch each year. The company has noted that when it charges more for each wristwatch, customers buy fewer of them that year. Its revenue from selling the wristwatches, in dollars, can be modeled by the expression p(1,080−6p)p(1,080 - 6p), where pp is the price per special-edition wristwatch in dollars. This expression can be written in factored form as −6p(p−180)-6p(p - 180).\newlineWhat does the number 180180 represent in the expression?\newline(A)Montox's maximum revenue in dollars\newline(B)Montox's minimum revenue in dollars\newline(C)the price per special-edition wristwatch in dollars that maximizes Montox's revenue\newline(D)the price per special-edition wristwatch in dollars so that Montox's revenue is zero\newline
  1. Factor revenue expression: The expression for revenue is p(1,080−6p)p(1,080 - 6p), which can be factored to −6p(p−180)-6p(p - 180).
  2. Set expression equal to zero: To find the meaning of 180180, set the factored expression equal to zero: −6p(p−180)=0-6p(p - 180) = 0.
  3. Solve for pp: Solve for pp when the revenue is zero: p=0p = 0 or p−180=0p - 180 = 0, which gives p=180p = 180.
  4. Find maximum price: The value p=180p = 180 is the price per wristwatch that makes the revenue zero when plugged into the original expression.
  5. Conclusion: Since increasing the price above 180180 would decrease the quantity sold to less than 00, which is impossible, 180180 is the maximum price before the revenue starts decreasing.
  6. Conclusion: Since increasing the price above 180180 would decrease the quantity sold to less than zero, which is impossible, 180180 is the maximum price before the revenue starts decreasing.Therefore, 180180 represents the price per special-edition wristwatch in dollars that maximizes Montox's revenue.

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