ANSWER
[tex]\begin{gathered} (a)\$9 \\ (b)\$8,100 \end{gathered}[/tex]EXPLANATION
(a) The revenue is gotten by finding the product of price and items sold.
Therefore, the revenue is:
[tex]\begin{gathered} R=x\cdot p \\ R=(1800-100p)\cdot p \\ R=1800p-100p^2 \end{gathered}[/tex]The function above is a quadratic function.
The find the price that will bring in the maximum revenue, we have to find the maximum value of the function.
The maximum value of a quadratic function is gotten by finding:
[tex]-\frac{b}{2a}[/tex]where a is the coefficient of p² and b is the coefficient of p.
Therefore, we have that the price at which the revenue is maximum is:
[tex]\begin{gathered} -\frac{1800}{2(-100)} \\ \Rightarrow-\frac{1800}{-200} \\ \Rightarrow\frac{1800}{200} \\ \Rightarrow\$9 \end{gathered}[/tex]That is the answer.
(b) The maximum revenue is the value of the revenue at the maximum price.
Therefore, the maximum revenue is:
[tex]\begin{gathered} R=(1800\cdot9)-(100\cdot9^2) \\ R=16200-8100 \\ R=\$8,100 \end{gathered}[/tex]