Problem $4.$ Las$-$O$-$Vision is the sole producer of holographic TVs$,3$DTVs$.$ The quality demand for $3$DTVs is

$q=10400-100p.$ The cost of producing $q3$DTVs per day is $C(q)=\frac{q^2}{4}.($Note this implies that $MC=\frac{dC(q)}{dq}=\frac{q}{2})$

$(20)$

$($a$)$ What is Las$-$O$-$Vision's total revenue schedule?

$($b$)$ What is Las$-$O$-$Vision's marginal revenue schedule?

$($c$)$ What is the profit$-$maximizing number of $3$DTVs that Las$-$O$-$Vision must produce each day? What price does

Las$-$O$-$Vision charge per $3$DTV$?$ What is its daily profit?