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Kevin writes and self-publishes his own quarterly sports magazine, The Fresh Catch. He has found that when he charges more per issue, he sells fewer issues overall that quarter. His revenue from selling the issues, in dollars, can be modeled by the expression p(9,000−1,500p)p(9,000 - 1,500p), where pp is the price per issue in dollars. This expression can be written in factored form as −1,500p(p−6)-1,500p(p - 6).\newlineWhat does the number 66 represent in the expression?\newline(A)the price per issue in dollars that maximizes Kevin's revenue\newline(B)the price per issue in dollars so that Kevin's revenue is zero\newline(C)Kevin's maximum revenue in dollars\newline(D)Kevin's minimum revenue in dollars

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Q. Kevin writes and self-publishes his own quarterly sports magazine, The Fresh Catch. He has found that when he charges more per issue, he sells fewer issues overall that quarter. His revenue from selling the issues, in dollars, can be modeled by the expression p(9,000−1,500p)p(9,000 - 1,500p), where pp is the price per issue in dollars. This expression can be written in factored form as −1,500p(p−6)-1,500p(p - 6).\newlineWhat does the number 66 represent in the expression?\newline(A)the price per issue in dollars that maximizes Kevin's revenue\newline(B)the price per issue in dollars so that Kevin's revenue is zero\newline(C)Kevin's maximum revenue in dollars\newline(D)Kevin's minimum revenue in dollars
  1. Rewrite expression: Rewrite the expression in factored form: −1,500p(p−6)-1,500p(p - 6).
  2. Identify zero points: Identify the zero points of the revenue function by setting the factored form equal to zero: −1,500p(p−6)=0-1,500p(p - 6) = 0.
  3. Solve for pp: Solve for pp: p=0p = 0 or p−6=0p - 6 = 0, which gives p=6p = 6.
  4. Interpret zero points: Interpret the zero points: p=0p = 0 means Kevin sells the magazine for $0\$0, which would result in no revenue. p=6p = 6 means that if Kevin charges $6\$6 per issue, the revenue will be zero because it's the point where the quantity sold drops to zero.
  5. Conclude significance of 66: Conclude what the number 66 represents: Since p=6p = 6 is the price at which revenue drops to zero, it is the price per issue in dollars that maximizes Kevin's revenue before it starts to decrease again.

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