Question

a firm estimates that it can sell q units of its product with an advertising expenditure of x thousand dollars when Q=Q(x) = -X2 +600x +25 i) over whta level of advertising expenditure is the number of units of products sold is incresing ? ii) over what level of advertising expenditure is the numbers of units of product sold decreasing?

Answer 1

Solution:

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

$\Rightarrow -2x+600 > 0 \\ \Rightarrow -x>-300 \\ \Rightarrow x<300$

Thus, $Q(x)$ is increasing for $-\infty<x<300$   

(ii) And decreasing for $300<x<\infty$

Here is the graph of Q(x).