Use the Activity$-$on$-$Arrow $($AOA$)$ diagram on the following page to determine the following $-$each number is the number of hours for the task.

a$.$ How many different paths are there through the network? $(15$ points$)$

b$.$ What is the number of the last node in the network? $(15$ points$)$

c$.$ What is the difference in hours taken for the two paths when they connect at node $10.(15$ points$)$

d$.$ What is the difference in hours taken for the two paths when they connect at node $12.(15$ points$)$

e$.$ What is the expected duration of the entire project? $(15$ points$)$

f$.$ What is the critical path? Separate each node with a dash $(-).$

$(12\mathrm{.}5$ points$)$