Answer
The number of radios that must be produced and sold is\[500\].
Work Step by Step
The revenue function is \[R\left( x \right)=50x\] and the cost function is \[C\left( x \right)=10000+30x\]. The break–even point occurs where the revenue and cost function intersect. So, to calculate the number of produced and sold radios for the break–even point,\[R\left( x \right)\] will be equal to \[C\left( x \right)\]. Therefore,
\[\begin{align}
& R\left( x \right)=C\left( x \right) \\
& 50x=10,000+30x \\
& 50x-30x=10,000 \\
& 20x=10,000
\end{align}\]
and
\[\begin{align}
& x=\frac{10,000}{20} \\
& x=500
\end{align}\]
The number of radios is \[500\].
Hence, the number of radios that must be produced and sold is \[500\].
