Question $4(25$ marks$)$

a$.$ Botho University is considering building a new sports complex on campus

to provide a new gymnasium for interuniversity games and classroom

purposes. The following activities and duration shown in the Table would

have to be undertaken before the project commences.

Required:

i$.$ Develop the activity on node $($AON$)$ network for this project. $(10$ marks$)$

ii$.$ Determine the critical path, project completion time using the forward and backward pass

methodology $(10$ marks$).$

b$.$ Mr$.$ Cyrus is faced with three options: to open a small shop, a medium$-$

sized shop, or no shop at all in Ukraine City near Bakmut to sell small

firearms. History has shown that the market for firearms provides payoffs

depending on whether the economy is in a boom, normal or recession. It

is estimated that the probabilities for boom, normal and recession are $0\mathrm{.}2,$

$0\mathrm{.}5$ and $0\mathrm{.}3,$ respectively. The corresponding profit or loss are shown in

the table below.

Use the expected monetary value to provide a recommendation to Mr$.$ Cyrus.