Question

A film maker wants to make and sell DVDs of a documentary film. It costs​ $6500 to make the film and​ $1500 to set up production. In​ addition, it costs​ $4 for each video made. Let​ P(n) be the price the film maker should set for each video so that it breaks even by making and selling n DVDs. Find​ P(500). What does it mean in this​ situation?

Answer 1

Explanation:

Cost to make the film : $6500

Cost to set up production: $1500

Additional cost to make each video : $4

Additional cost to make n videos : $4n

total cost to make n videos = $6500 + $1500 + $4n = (8000 + 4n) dollars

overall cost to make each video

= total cost to make n videos ÷ n videos

= (8000 + 4n) / n

by definition, in order to "break even", the selling price for each video must be equal to the cost to make each video. i.e

Price, P(n) = (8000 + 4n) / n

Hence,

P(500) = [8000 + 4 (500)] / 500 = (8000 + 2000) / 500 = $20

This means that in order to break even selling 500 DVD's he has to sell each one for $20