$(SHOW$ ALL WORK$)$

Given the $SRcost$ curves functions $TC(Q)=\frac{Q^3}{6}-30Q^2+1820Q+400,$ and, $MC(Q)=\frac{Q^2}{2}-60Q+1820$ :

aTFC$(Q),TVC(Q),$ATC$(Q),$ and AVC$(Q)$ functions.

$bQ=64(i.e.,$ calculate $TC(64),MC(64),TVC(64),$ ATC$(64),$

AVC$(64),$ and AFC$(64).$

$c)$ Calculate the quantity $at$ which AVC $isat$ a minimum.

$d$