You are requested to design a column for $P_D=200k$ and $P_L=400k,$ using A$992$ steel with $KL=16ft.$ A W$14$x$68$ is available but may not provide sufficient capacity. If it does not, cover plates may be added to the section to increase the W$14\text{'}$s capacity. Design the cover plates to be $12$ inch wide and welded to the flanges of the section to enable the column to support the required load $($see the below figure, assume the welds are continuous along the two sides of the cover plates$).$ Determine the minimum plate thickness required, assuming the plates are available in $\frac{1}{16}$ th$-$in increments.