finite math

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?

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  1. revenue = price * copies
    profit = revenue - cost, so

    y = pq - 4q
    = (240000-15000p)(p-4)
    = 15000(16-p)(p-4)
    = 15000(-p^2+20p-64)

    That's just a parabola with vertex at p=10.

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