You may need to use the appropriate technology to answer this question.

A project consists of five activities as shown in the following table.

Activity Optimistic Time $($hr$)$ Most Probable Time $($hr$)$ Pessimistic Time $($hr$)$

Floor sanding $456$

Floor buffing $456$

Paint mixing $0\mathrm{.}511\mathrm{.}5$

Wall painting $3411$

Ceiling painting $37\mathrm{.}59$

Naturally, the paint mixing precedes the painting activities. Also, both ceiling painting and floor sanding must be done prior to floor buffing.

$($a$)$

Construct the PERT$/$CPM network for this problem.