Reference the framing plan below to answer the following questions:

$($a$)$ The residence shown is constructed of $24$ lumber and includes a single treated sole plate and two top plates. Determine the purchase quantity and number of board feet of treated and untreated lumber needed f$$r the wall plates on only the exterior wall. Do not subtract any length for doorway openings.

$($b$)$ Determine the number of $8-ft$ long $-24$ studs needed for the exterior wall. The studs are spaced $16$ inches on center. Add $3$ additional studs for each door and window and $2$ additional studs for each corner. Ignore interior walls.