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 = 220,000 − 11,000p copies. What price will bring in the greatest revenue? HINT [See Example 3.]

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01-04-2020
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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 = 220,000 − 11,000p copies. What price will bring in the greatest revenue? HINT [See Example 3.]

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Answer:

The price of 10 brings the greatest revenue or it is the price at which revenue is maximized.

Explanation:

The revenue is a function of Price multiplied by quantity. The revenue equation for the Hercules films is:

Revenue = Price * Quantity sold

Revenue = p * (220000 - 11000p)

Revenue = 220000p - 11000p²

We need to calculate the price at which revenue is maximized and as price changes, the quantity and revenue are changing. Thus we need to find the derivative of this equation to calculate the value of p.

d/dp = 1 * 220000p° - 2 * 11000p

Where p° = 1

0 = 220000 - 22000p

22000p = 220000

p = 220000 / 22000

p = 10

Thus p = 10 or price is 10 when revenue is mazimized.