Recently, you were assigned to manage a project for your company. You have constructed a network diagram depicting the various activities in the project$($shown below to the$$ right$).$ In$$ addition, you have asked your team to estimate the amount of time that they would expect each of the activities to take. Their responses are shown in the following$$ table:

Time Estimates$($days$)$

StartFinishABCDE

In the diagram, there are $2$ rectangles. The one on the left is labeled Start, and the one on the right is labeled Finish. There are $5$ circles labeled inside each circle using the letters from A to E$.$ There is a number below the letter inside each circle. There are arrows to indicate flows from Start to Finish as follows: Rectangle Start has arrows that connect it to circle A and to circle B$,$ circle A connects to circle C and to circle D$,$ circles B and D both connect to circle E$,$ and circles C and E both connect to rectangle Finish.

Activity

Optimistic

Most Likely

Pessimistic

A

$6$

$7$

$12$

B

$5$

$7$

$10$

C

$4$

$6$

$8$

D

$1$

$5$

$6$

E

$4$

$8$

$11$

Part $2$

a$.$ What is the expected completion time of the$$ project?

The expected completion time is

days. $($Enter

your response as an integer$.)$