The following exercise involves the information in the figure shown below on constructing a home.

Task Length Dependency

a$.$ Write and agree on contracts $3$ weeks

b$.$ Secure financing $4$ weeks a

c$.$ Obtain permits $6$ weeks a$,$ b

d$.$ Site work $4$ weeks a$,$ b$,$ c

e$.$ Build foundation $3$ weeks b$,$ c$,$ d

f$.$ Erect walls $3$ weeks d$,$ e

g$.$ Build roof $5$ weeks f

h$.$ Rough in plumbing $2$ weeks f

i$.$ Rough in electrical $2$ weeks f

j$.$ Rough in furnace and air conditioning $1$ week f

k$.$ Finish exterior $6$ weeks f$,$ g$,$ i

l$.$ Finish interior $6$ weeks f$,$ g$,$ h$,$ i$,$ j

m$.$ Finish plumbing $2$ weeks h$,$ i

n$.$ Finish electrical $1$ week i$,$ l

o$.$ Finish furnace and air conditioning $1$ day j$,$ l

p$.$ Wait for inspection $2$ weeks k$,$ l$,$ m$,$ n$,$ o

If the project proceeds on schedule, how much time should have elapsed before the roof is built? If appropriate, give a range of time.

Roof building should begin after

weeks and should end after

weeks.