Answer
$(6,300)$.
Work Step by Step
The given revenue function is
$\Rightarrow R(x)=50x$
Let $R(x)=y$
$\Rightarrow y=50x$
Let $x=0$.
$\Rightarrow y=50(0)$
$\Rightarrow y=0$
One point is $A=(0,0)$
Let $x=1$.
$\Rightarrow y=50(1)$
$\Rightarrow y=50$
Second point is $B=(1,50)$
Now draw a straight line containing both points.
The given cost function is
$\Rightarrow C(x)=20x+180$
Let $C(x)=y$
$\Rightarrow y=20x+180$
Let $x=0$.
$\Rightarrow y=20(0)+180$
$\Rightarrow y=180$
One point is $C=(0,180)$
Let $x=1$.
$\Rightarrow y=20(1)+180$
$\Rightarrow y=20+180$
$\Rightarrow y=200$
Second point is $D=(1,200)$
Now draw a straight line containing both points.
The intersection point of both lines is the break even point.
In the below graph the break even point is $(6,300)$.
