Question

How many DVDs. A small independent movie company determines the profit P for producing n DVD copies of a recent release is P = −0.02n2 + 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?

should the company produce to maximize the profit?

Answer 1

The company should produce "85" DVD's to maximize the profit.

According to the question,

The profit P for producing n DVD copies are

• $P=-0.02n^2+3.4n -16$

Let,

• The number of units be "n".

Now,

To find the minimize profit,

→ $P'(n) = 0$

→ $-0.04n+3.4=0$

By substracting "3.4" from both the sides, we get

→ $-0.04n+3.4-3.4=-3.4$

→                   $-0.04n = -3.4$

→                            $n = \frac{-3.4}{-0.04}$

→                            $n = 85$

Thus the answer above is right.

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