Question

Hercules films is also deciding on the price of the video release of its film bride of the son of frankenstein. again, marketing estimates that at a price of p dollars, it can sell q 5 200,000 2 10,000p copies, but each copy costs $4 to make.

what price will give the greatest profit?
p=______dollars

Answer 1

To maximize profit, Hercules Films should set the price of the video release to $12. This was determined by deriving and analyzing the profit function associated with production and selling cost.

Step-by-step explanation:

To determine the price P that maximizes profit for Hercules Films, we need to analyze the profit function. The company's revenue (R) is the product of price (P) and quantity sold (Q), which according to the question's equation is 200,000 - 10,000P. Subtracting the cost to make each copy, we get the profit (Π) function:

Π(P) = P * (200,000 - 10,000P) - 4 * (200,000 - 10,000P)

Expanding this, we get:

Π(P) = 200,000P - 10,000P^2 - 800,000 + 40,000P

Simplifying:

Π(P) = -10,000P^2 + 240,000P - 800,000

To find the price that maximizes profit, take the derivative of Π with respect to P and set it equal to zero:

Π'(P) = -20,000P + 240,000 = 0

Solving for P:

P = 240,000 / 20,000

P = $12

Therefore, setting the price at $12 will yield the greatest profit for Hercules Films.