Problem $3$: A Monopoly Example $[8$ Points$]$

Consider a firm which acts as a Monopolist. This firm has the following Cost Curve:

$TC=40+0\mathrm{.}5Q^2$

Which implies that:

$MC=Q$

This market also has the following Demand Curve:

$Q=200-4p$

What is this monopolist's Marginal Revenue Curve as a function of $Q?[1$ point$]$

What is this monopolist's Profit$-$Maximizing choice of $p$ and $Q?[2$ points$]$

What is the Producer Surplus $($PS$),$ Consumer Surplus $($CS$),$ and Deadweight Loss $($DWL$)$ under this monopoly? $[3$ points$]$

What is this monopolist's $($maximized$)$ accounting profits? Why is this not equal to their Producer Surplus? $[2$ points$]$