Answer to Question #203854 in Financial Math for Muhammad Asad Ali

Question

A firm estimates that it can sell Q units of its product with an advertising expenditure of x thousand dollars where

Q = Q(x)=x² + 600x + 25

i) Over what level of advertising expenditure is the number of units of

product sold increasing?

ii) Over what level of advertising expenditure is the number of units of product sold decreasing?

Answer 1

We are given that Q(x)=x² + 600x + 25.

(i),

We need to find over what level of advertising expenditure is the number of units of product sold increasing.

Now,

     Q'(x) = 2x+600.

For increasing,

          Q'(x)>0

      => 2x+600 > 0

      => x>-300

Let us plot the graph of Q(x).

It can be observed that for all x>0 the function Q(x)>0.

Further, the advertising expenditure is x thousand dollars and is always positive.

So, the answer to (I) is x>0 and the answer to (ii) is DNE.