Problem B $(50$ points$)$

Two workers are carrying a $2-$in$-$thick panel by means of panel carriers, one of which is shown in the detail figures below. The vertical panel is steadied by equal horizontal forces applied by the left hands of the workers, which are $30$ inches above point $\backslash ($ B $\backslash )$ on the carrier. Determine the minimum coefficient of static friction between the panel and the carriers for which there will be no slippage. The carrier grips at $\backslash ($ A$,$ B $\backslash ),$ and $\backslash ($ C $\backslash )$ do not rotate on the carrier frame. Note that each worker must apply both a vertical and a horizontal force to the carrier handle. Assume that each worker supports half the weight of the panel and that the weight of the carriers is negligible.