A manufacturer of tablet computers, after extensive research established the following price-demand, and cost functions:
$p(x)= 360-20x$
$c(x)= 300+95x$
where $p(x)$ is the wholesale price in dollars at which $x$ million tablet computers can be sold. The cost $c(x)$ is in millions of dollars. The domain of each function is $1 < x < 15$.
A) Find the revenue function $R(x)$ and sketch the graph of $R(x)$.
B) Find the output which will produce the maximum revenue. What is the maximum revenue? What is the wholesale price, per tablet computer, that produces the maximum revenue?
C) For what outputs will a loss occur? For what outputs will a profit occur?
Best Answer
This is just an addition to my comment. As André Nicolas and I showed you, you can obtain your revenue function $R(x)$ by multiplying price $p(x)$ by the quantity $x$
$$R(x)=p(x)\cdot x=(360-20x)x=360x-20x^2$$
Graph:
b) you should be able to solve with some elementary calculus and for c) you should try to find $x$'s for which Cost $>$ Revenue
Edit:
For b), setting $$p(x)=c(x)$$
will not give you the maximum revenue. You can even see this by looking at the graph.
The break-even point $p(x)=c(x)$ occurs after maximum revenue has been reached.