Indy Pool Installers $($A$)$

Indy Pool Installers is about to work on a project to install a backyard pool and build an

accompanying bathhouse. The installation process is fairly well defined. Building the pool

involves digging the foundation, pouring concrete, and ordering and installing a filtration system.

The bathhouse work involves constructing of the bathhouse, installing the additional required

plumbing, and installing the necessary electrical work.

Each of the following is a task in the project.

The pool installation starts with digging the foundation, a process that usually takes $10$ days.

Indy can also order the filtration system from their supplier at this point, a relatively simple $1$

day operation.

Indy has to wait another $9$ days while the system is being shipped before it is received. Since

the "waiting" task involves no manpower, unlike the ordering task, Indy considers it separate

from the ordering task in their project planning process.

Pouring concrete into the dug foundation usually requires $3$ days.

Installation of the filtration system requires $13$ days. The filtration system can not be installed

until after the concrete has been poured.

Construction of the bathhouse is fairly involved, requiring $23$ days. Work can begin or this

immediately.

After the basic bathhouse structure is up$,$ an electrician is able to run wire from the main house

to the bathhouse. This should take $2$ days.

After the basic bathhouse structure is up$,$ a water line can be laid from the main house to the

bathhouse. This should take $3$ days.

Connecting the installed water line to the main house water supply involves another $2$ days.

A final test of all the electrical work, water work, and filtration system takes $2$ days.