Answer
The company could go ahead with production of new product.
The profit function $P(x)=145x-6000$
Work Step by Step
Substituting for $R(x)$ and $C(x)$ in the equation $R(x)=C(x)$ gives
$105x+6000=250x$
$145x=6000$
$x \approx 41$
The firm breaks even by selling 41 units, which is the break-even quantity.
If the company sells more than 41 units, it makes a profit.
Since there is no more than 400 units can be sold, the company can make a profit manufacturing new product as long as the number of selling units between 41 and 400.
The profit function P(x)
$P(x)=R(x)-C(x)$
$P(x)=250x-105x-6000$
$P(x)=145x-6000$
