Question 1119854: 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 = 200,000-20,000p copies. What price will bring in the greatest revenue?
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
The revenue = the product of the price by the quantity sold: R = p*q, or
R = p*(200000-20000*p) = 20000*p*(10-p).
The roots of this quadratic function are p= 0 and p= 10; hence, the maximum of the quadratic function is located
exactly half way between the roots, i.e. at p= 5.
Answer. The price p= 5 dollars per video provides the maximum revenue.
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