Problem $1$

Consider the set of activities, durations $($in days$),$ and predecessors for the project in the table below:

$\backslash$table$[[$Activity$,$A$,$B$,$C$,$D$,$E$,$F$,$G$],[$Duration$,3,5,2,4,6,3,2],[$Predecessors$,-,-,$A$,$B$,$ C$,$A$,$C$,$ E$,$B$]]$

Develop a dependency diagram representing the project's activities.

Identify all paths to project completion.

Determine the critical path$($s$)$ and the total project duration.

Problem $2$

Using the network diagram provided below:

Identify all paths to project completion.

Determine the critical path.

Determine the float time for all activities in the network.

Problem $3$

A new portable charger is being developed. The following information is available:

Development cost: $100,000KD,$

Production investment: $700,000$ KD$,$

Variable cost: $8$ KD per unit,

Annual production volume: $60,000$ units,

Sales lifetime: $5$ years.

Determine the minimum sales price to break even in $14$ months

Using your answer in part $1,$ determine the total profit over the product's sales lifetime

Hint: monthly production $=\frac{\text{A}\text{n}\text{n}\text{u}\text{a}\text{l}\text{p}\text{r}\text{o}\text{d}\text{u}\text{c}\text{t}\text{i}\text{o}\text{n}}{12}$