Answer
$(6,300)$.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/fa1c5c0e-a4b3-4f26-8d64-b4e77e4dc446/result_image/1635924434.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000336Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2a8006220132397581b3b1c5642fe5afc02d85c0424b6dd67ae1aff6ebbcdd52)
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 $(6,300)$.