$7.$ The following table refers to a project in which the objective is to raise capital for a commercial building activity.

ACTIVITY DURATION $($Days$)$ PREDECESSORS

A $7-$

B $4-$

C $5$ A$,$ B

D $19$ C

E $9$ C

F $7$ E

G $10$ C

H $5$ D$,$ E$,$ G

I $8$ G$,$ F

J $5$ H

K $29$ I, J

For parts a and b below you can use MS Project if you so desire. If you do so$,$ please cut and paste the relevant pages from MS Project $($do not send me the whole MS Project file$)$

a$.$ Draw a network diagram of the project

b$.$ Identify the critical path, its duration and the activity slacks.

Consider the additional Time$/$Cost trade$-$off data.

ACTIVITY Normal Duration Normal cost Crash Duration Crash Cost

A $7$ $$3,0004$ $$4,500$

B $45,00025,350$

C $56,0005($cannot crash$)-$

D $1920,0001629,000$

E $910,000712,000$

F $77,00068,000$

G $1020,000826,000$

H $58,000410,000$

I $85,00075,600$

J $57,00047,650$

K $2912,0002318,000$

c$.$ Assume the overhead costs for this project are $$700$ per day. What is the optimal crashing strategy? Please describe you crashing strategy step$-$by$-$step.

d$.$ What is the optimal project duration? What are the critical paths as a result of your crashing?