Problem $2(20$ points$)$

Using Figures $2-1$ and $2-2$:

The residence is constructed of $24$ lumber and includes a single treated bottom $($sole$)$ plate and two untreated top plates. Determine the purchase quantity and number of board feet of treated and untreated lumber needed for the wall plates. Ignore the openings.

Determine the number of $24$@${16}^{\text{'}\text{'}}$ studs needed for the residence. The studs are spaced $16$ inches on center. Add two studs for each door, window, intersection, and corner. Ignore the gable ends.

Determine the materials needed for the headers for the residence. Two $210$ s are used for the headers in the exterior walls and the wall running east$-$west through the house. The remaining headers are two $24$ s$.$ The swinging doors are $3$ feet wide and the closet doors are $6$ feet wide. Allow $2\mathrm{.}5$ in of bearing on each side for doors, and $1\mathrm{.}5$ in of bearing on each side for windows.

Determine the number of $8-$foot$-$long studs needed for the gable ends of the residence. The gable end on the east elevation is the same as the gable end on the west elevation. Ignore the door and window openings because this material will be waste.

Determine the number of $4-$foot by $8-$foot sheets of plywood needed to cover the exte rior of the residence.