Answer
The value of \[R\left( 300 \right)-C\left( 300 \right)\] is,\[-4000\] and it represents that when the company produces and sells\[300\]radios. The loss is,\[-4000\].
Work Step by Step
The profit function \[P\left( x \right)\] is the difference between \[R\left( x \right)\]and \[C\left( x \right)\]. Therefore,
\[P\left( x \right)=R\left( x \right)-C\left( x \right)\].
When \[P\left( x \right)\] is positive then it represents the profit and if \[P\left( x \right)\] is negative then it represents the loss.
The value of the profit function is,
\[\begin{align}
& P\left( x \right)=R\left( x \right)-C\left( x \right) \\
& =50x-\left( 10000-30x \right) \\
& =50x-10000-30x \\
& =20x-10000
\end{align}\]
The value of the profit function is, \[P\left( x \right)=20x-10000\]
Put \[x=300\]in \[P\left( x \right)=20x-10000\]. Then, the value of \[P\left( 300 \right)\] is,
\[\begin{align}
& P\left( x \right)=20x-10000 \\
& =20\times 300-10000 \\
& =6000-10000 \\
& =-4000
\end{align}\]
Hence, the value of \[P\left( x \right)\] is \[-4000\] when the \[300\] small radios produced and sold. As \[P\left( x \right)=-4000\] represent the loss of \[-4000\] when the \[300\] radios produced and sold.
