be $P=600-3Q,$ where $P$ denotes price in dollars and $Q$ denotes total unit sales. The firm's cost equation is $TC=3,200+50Q+2Q^2.$

a$.$ Derive the equations for marginal revenue and marginal cost.

$2$ points

b$.$ Determine the dollar values for Marginal Revenue $($MR$),$ and Marginal Cost $($MC$)$ if the firm is currently producing at an output level $($Q$)$ of $75$ units.

$2$ points

c$.$ Provide a recommendation to this firm if they should increase, decrease, or keep the quantity at $Q=75$ to maximize its profit $($you must motivate your answer$)?$

$1$ point

d$.$ How should this firm change $($increase$,$ decrease, or keep the same$)$ its profit maximizing quantity compared to your finding in part $c$ if the firm's fixed cost changes from $3,200$ to $3,800$ so $TC=3,800+50Q+2Q^2($you must motivate your answer$)?$

$1$ point

e$.$ How should this firm change $($increase$,$ decrease, or keep the $)$ its profit maximizing quantity compared to your finding in part $c$ if the firm's variable cost changes so $TC=3,200$