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 = 300,000 − 15,000p copies, but each copy costs $4 to make. What price will give the greatest profit?

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 = 300,000 − 15,000p  copies, but each copy costs $4 to make. What price will give the greatest profit?

anonymous · Answer

So, for a given price, p, we'll sell q units, at a profit of P.
q=300000−15000p
P=q∗(p−4)=(300000−15000p)(p−4)

If you expand P and find the vertex, you'll have the best price. If you can use calculus, take the derivative of P with respect to p and set it equal to 0. Solve for p and you have your answer.