The following table represents a plan for a project:

TIMES $($DAYS$)$

JOB NO$.$ PREDECESSOR

JOB$($S$)$ a m b

$1234$

$21123$

$314512$

$413411$

$52135$

$63123$

$74189$

$85,6246$

$982412$

$107345$

$119,10578$

b$.$ Indicate the critical path. multiple choice $1$

$1-2-5-8-9-11$

$1-4-7-10-11$

$1-3-6-8-9-11$

c$.$ What is the expected completion time for the project? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

d$.$ You can accomplish any one of the following at an additional cost of $$1,500.$ If you will save $$1,000$ for each day that the earliest completion time is reduced, which of the following actions should be taken, if any?

$1.$ Reduce job $5$ by two days.

multiple choice $2$

Yes

No

$2.$ Reduce job $3$ by two days.

multiple choice $3$

Yes

No

$3.$ Reduce job $7$ by two days.

multiple choice $4$

Yes

No

e$.$The following CPM network has estimates of the normal time in weeks listed for the activities:

a$.$ Identify the critical path.

multiple choice $1$

A$-$C$-$D$-$F$-$G

A$-$B$-$D$-$E$-$G

A$-$C$-$D$-$E$-$G

A$-$B$-$D$-$F$-$G

b$.$ What is the length of time to complete the project?

c$.$ Which activities have slack, and how much?

multiple choice $2$

C$,2$ weeks; F$,3$ weeks.

D$,1$ week; E$,2$ weeks.

B$,2$ weeks; E$,2$ weeks.

C$,1$ week; E$,2$ weeks.

Here is a table of normal and crash times and costs.

ACTIVITY NORMAL TIME CRASH TIME NORMAL

COST CRASH

COST

A $76$ $ $7,000$ $ $8,000$

B $215,0007,000$

C $439,00010,200$

D $543,0004,500$

E $212,0003,000$

F $424,0007,000$

G $545,0008,000$

d$-1.$ Which activities would you shorten to cut two weeks from the schedule in a rational fashion?

multiple choice $3$

B$,$ D

A$,$ C

B$,$ C

A$,$ E What is the probability that the project will take more than $30$ days to complete? $($Use Excel's NORMSDIST$()$ function to find the correct probability for your computed Z$-$value. Other than the expected completion time you entered in part c above, do not round intermediate calculations. Round $"$z$"$ value to $2$ decima