Question

Hercules Films is deciding on the price of the video release of its film Bride of the Son of Frankenstein. Marketing estimates that at a price of p dollars, it can sell
q = 240,000 − 15,000p
copies, but each copy costs $4 to make. What price will give the greatest profit?

Answer 1

Profit =S(p)= q*p - 4q = 240000p - 15000p² + 60000p - 960000 = 300000p - 15000p² - 960000

S'(p) = 300000 - 30000p = 0 -> p = 10

So the price that gives the greatest profit is $10

Answer 2

Given the information:

$q= 240000 - 15000p$, where $C = 4 each copy$

So:

$Profit =S(p)= q*p - 4q$

$Profit = 240000p - 15000p^{2} + 60000p - 960000$

$Profit = = 300000p - 15000p^{2} - 960000$

$S'(p) = 300000 - 30000p = 0 \rightharpoonup p = 10$

Finally, the price that gives the greatest profit is $10.

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