A small independent motion picture company determines the profit P for producing n DVD copies of a recent release is P = -0.02n^2 + 3.40n - 16. P is the profit in thousands of dollars and n is in thousands of units.
a. How many DVDs should the company produce to maximize the profit?
b. What will the maximize profit be?

I don't understand what it means by "maximize the profit."

Question

A small independent motion picture company determines the profit P for producing n DVD copies of a recent release is P = -0.02n^2 + 3.40n - 16. P is the profit in thousands of dollars and n is in thousands of units.
a.	How many DVDs should the company produce to maximize the profit?  
b.	What will the maximize profit be? 


I don't understand what it means by "maximize the profit."

anonymous · Answer

Maximize the profit is pretty much saying what will be the maxed profit that you can produce with the equation or what will the profit be after n number of units.

anonymous · Answer

So would I set the equation equal to 0?

anonymous · Answer

$$ P = -0.02n^2 + 3.40n - 16$$ is a parabola that opens down
the maximum is therefore at the vertex, which is what you are being asked to find

anonymous · Answer

the first coordinate of the vertex of 
$$y=ax^2+bx+c$$ is 
$$-\frac{b}{2a}$$ and the second coordinate is what you get for $y$ when you replace $x$ by $-\frac{b}{2a}$

anonymous · Answer

How would I get the number of DVD's from the vertex, though?