Answer
See below:
Work Step by Step
(a)
The company’s cost and revenue functions are given as \[C\left( x \right)\]and \[R\left( x \right)\], respectively.
The profit function \[P\left( x \right)\] of the company can be found by subtracting the cost function from the revenue function:
\[P\left( x \right)=R\left( x \right)-C\left( x \right)\]
Substitute the values for cost and revenue function.
\[\begin{align}
& P\left( x \right)=50x-\left( 10,000+30x \right) \\
& =20x-10,000
\end{align}\]
Thus, the obtained revenue function is\[P\left( x \right)=20x-10,000\].
(b)
The profit function \[P\left( x \right)\] of the company can be found by subtracting the cost function from the revenue function.
\[P\left( x \right)=R\left( x \right)-C\left( x \right)\]
Thus, apply the above formula:
\[\begin{align}
& P\left( x \right)=50x-\left( 10,000+30x \right) \\
& =20x-10,000
\end{align}\]
Here, \[x\] is the number of units produced and sold. Therefore, substitute \[10,000\]for\[x\]:
\[\begin{align}
& P\left( 10,000 \right)=20\left( 10,000 \right)-10,000 \\
& =200,000-10,000 \\
& =\$190,000\end{align}\]
Thus, the profit of the company is\[\$190,000\].
