Question

The revenue from the sale of a product is given by the function R=400x−x3. Selling how many units will give positive revenue?

Answer 1

ANSWER:

Selling more than 0 and less than 20 units will give positive revenue.

STEP-BY-STEP EXPLANATION:

We have the following function:

$R=\: 400x-x^3$

Now, we propose the following inequality:

$\begin{gathered} 400x-x^3>0 \\ \text{ solving for x:} \\ x\cdot(400-x^2)>0 \\ x\cdot(x-20)\cdot(x+20)>0 \\ \text{ therefore:} \\ x>0 \\ x-20>0\rightarrow x>20 \\ x+20>0\rightarrow x>-20 \\ \text{ in interval form:} \\ (-\infty,-20)\cup(0,20) \end{gathered}$

Since negative units cannot be sold, we are then interested in the range from 0 to 20, therefore, if more than 0 and less than 20 units come in, the revenue will be positive.