Problem $1[25$ pts$]$:

A four$-$bladed ceiling fan has $3-$ft by $\backslash (0\mathrm{.}2-\backslash$mathrm$\{$ft$\}\backslash )$ equally spaced rectangular blades that nominally weigh $4$ lbs each. Manufacturing tolerances will cause the blade weight to vary up to plus or minus $\backslash (10\backslash \%\backslash ).$ Calculate the weight of the counterweight needed at a $4-$in radius to statically balance the worstcase blade assembly. The distance between the center of rotation and the inner edge of the blades is $8$ in $.$