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Question 425780: I need to find a profit function out of this word problem:
Hercules Films is also deciding on the price of the video release of it's film Bride of the son of Frankenstein. Again, marketing estimates that at a price of p dollars it can sell q=324000-18000p copies, but each copy cost $4 to make. What price will give the greatest profit?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Hercules Films is also deciding on the price of the video release of it's film Bride of the son of Frankenstein. Again, marketing estimates that at a price of p dollars it can sell q=324000-18000p copies, but each copy cost $4 to make. What price will give the greatest profit?
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Profit = Revenue-Cost
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Revenue = p(324000-p)
Cost = 4p
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Profit = p(324000-p)-4p
Profit = 323996p - p^2
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That is a quadratic with a = -1 and b = 323996
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Maximum profit occurs when p = -b/(2a) = -323996/(-2) = $161,998
That price will give the greatest profit.
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Cheers,
Stan H.
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