Hercules films is deciding on the price of the video release of its film "Son of Frankenstein". Its marketing people estimate that at a price of p dollars, it can sell a total of $q = 10,000 - 200 p$ copies. What price will bring in the greatest revenue Round your answer to the nearest cent
A)$25.75
B) $25.00
C) $37.50
D) $24.50
E) $77.25

Question

Hercules films is deciding on the price of the video release of its film "Son of Frankenstein". Its marketing people estimate that at a price of p dollars, it can sell a total of $q = 10,000 - 200 p$ copies. What price will bring in the greatest revenue  Round your answer to the nearest cent 
A)$25.75
B) $25.00
C) $37.50
D) $24.50
E) $77.25

Quizplus · Accepted Answer

Revenue $R$ is given by the product of price $p$ and quantity $q$, so $R = p(10,000 - 200p)$. To maximize revenue, differentiate $R$ with respect to $p$ and set the derivative equal to zero. The derivative of $R$ with respect to $p$ is $10,000 - 400p$. Setting this equal to zero gives $10,000 - 400p = 0$, which simplifies to $400p = 10,000$ and further to $p = 25$. Therefore, the price that will bring in the greatest revenue is $25.00.

Hercules Films Is Deciding on the Price of the Video q=10,000−200pq = 10,000 - 200 pq=10,000−200p

Hercules Films Is Deciding on the Price of the Video $q = 10,000 - 200 p$