Answer
The number of radios must be produced and sold is greater than\[500\].
Work Step by Step
The company produced and sold radios should be greater than for the break-even point. The revenue function is \[R\left( x \right)=50x\]and \[C\left( x \right)=10000+30x\]. 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,
\[\begin{align}
& R\left( x \right)=C\left( x \right) \\
& 50x=10000+30x \\
& 50x-30x=10000 \\
& 20x=10000
\end{align}\]
Or:
\[\begin{align}
& x=\frac{10000}{20} \\
& x=500
\end{align}\]
Hence, the number of radios must be produced and sold is more than\[500\].
