Answer
$P(x)=20x-900$
The company should not go ahead with production of new product
Work Step by Step
Substituting for $R(x)$ and $C(x)$ in the equation $R(x)=C(x)$ gives
$85x+900=105x$
$20x=900$
$x=45$
The firm breaks even by selling 45 units, which is the break-even quantity.
If the company sells more than 45 units, it makes a profit.
Since there is no more than 38 units can be sold, the company doesn't make a profit manufacturing new product. Hence, it should not go ahead with production of new product
The profit function $P(x)$
$P(x)=R(x)-C(x)$
$P(x)=105x-85x-900$
$P(x)=20x-900$
