Problem

$1$

: Given the information provided below

$($

predecessors

$,$

$$normal time, normal cost, crash time

$($

the minimum duration

$)$

$$and crash cost

$($

the cost if crashed to the minimum duration

$)$

$$for an nine

$-$

activity

$($

a to i

$)$

$$project

$)$

$$answer the questions

$($

a

$)$

$$through

$($

e

$)$

$$using this template. You need to provide enough explanations to show evidence that you have understood this topic.

$$

Activity Predecessor Normal Time Normal Cost Crash Time Crash Cost

a

$-$

$4$

$$ $

$5$

$0$

$2$

$$ $

$1$

$5$

$0$

$$

b a

$4$

$$ $

$4$

$0$

$2$

$$ $

$2$

$0$

$0$

$$

c b

$7$

$$ $

$7$

$0$

$4$

$$ $

$1$

$6$

$0$

$$

d c

$,$

$$f

$2$

$$ $

$2$

$0$

$1$

$$ $

$5$

$0$

$$

e c

$3$

$$ $

$3$

$0$

$2$

$$ $

$1$

$0$

$0$

$$

f b

$8$

$$ $

$8$

$0$

$5$

$$ $

$2$

$9$

$0$

$$

g d

$,$

$$e

$5$

$$ $

$5$

$0$

$3$

$$ $

$1$

$0$

$0$

$$

h f

$6$

$$ $

$6$

$0$

$2$

$$ $

$1$

$8$

$0$

$$

i g

$,$

$$h

$3$

$$ $

$5$

$0$

$3$

$$ $

$5$

$0$

$$

$$

$$

$($

a

$)$

$.$

$$Create the network diagram in the application of your choice and then insert a screen shot of the diagram here. The diagram can be created easily in MS Word using the Insert Shapes function.

$$

$$

$[$

a

$]$

$$

$|$

$$

$[$

b

$]$

$$

$|$

$$

$[$

c

$]$

$-$

$-$

$-$

$-$

$-$

$-$

$[$

e

$]$

$$

$|$

$|$

$$

$[$

f

$]$

$-$

$-$

$-$

$-$

$-$

$-$

$-$

$|$

$$

$$

$|$

$|$

$$

$[$

d

$]$

$-$

$-$

$-$

$-$

$-$

$-$

$[$

g

$]$

$$

$|$

$$

$[$

h

$]$

$$

$|$

$$

$[$

i

$]$

$$

Identify the critical path of the network, the time, and cost of the normal level of activity for the project:

$$

$$The critical path

$($

or paths

$)$

$$is:

Path

$1$

: a

$-$

$>$

$$b

$-$

$>$

$$c

$-$

$>$

$$d

$-$

$>$

$$g

$-$

$>$

$$i

Duration:

$4$

$+$

$4$

$+$

$7$

$+$

$2$

$+$

$5$

$+$

$3$

$=$

$2$

$5$

$$days

Path

$2$

: a

$-$

$>$

$$b

$-$

$>$

$$c

$-$

$>$

$$e

$-$

$>$

$$g

$-$

$>$

$$i

Duration:

$4$

$+$

$4$

$+$

$7$

$+$

$3$

$+$

$5$

$+$

$3$

$=$

$2$

$6$

$$days

Path

$3$

: a

$-$

$>$

$$b

$-$

$>$

$$f

$-$

$>$

$$d

$-$

$>$

$$g

$-$

$>$

$$i

Duration:

$4$

$+$

$4$

$+$

$8$

$+$

$2$

$+$

$5$

$+$

$3$

$=$

$2$

$6$

$$days

Path

$4$

: a

$-$

$>$

$$b

$-$

$>$

$$f

$-$

$>$

$$h

$-$

$>$

$$i

Duration:

$4$

$+$

$4$

$+$

$8$

$+$

$6$

$+$

$3$

$=$

$2$

$5$

$$days

The critical path is Path

$2$

$$and Path

$3$

:

Critical Paths: a

$-$

$>$

$$b

$-$

$>$

$$c

$-$

$>$

$$e

$-$

$>$

$$g

$-$

$>$

$$i and a

$-$

$>$

$$b

$-$

$>$

$$f

$-$

$>$

$$d

$-$

$>$

$$g

$-$

$>$

$$i

$$

$$The project duration:

$2$

$6$

$$days

$$

$$The project cost is: $

$4$

$5$

$0$

The normal project cost is calculated by summing the normal costs of all activities:

$5$

$0$

$+$

$4$

$0$

$+$

$7$

$0$

$+$

$2$

$0$

$+$

$3$

$0$

$+$

$8$

$0$

$+$

$5$

$0$

$+$

$6$

$0$

$+$

$5$

$0$

$=$

$4$

$5$

$0$

$$

$($

b

$)$

$.$

$$Calculate the crash cost

$-$

per

$-$

day

$($

all activities may be partially crashed

$)$

$.$

$$Enter your response to question

$1$

$($

b

$)$

$$in the table provided below

$$

Activity Normal Time Normal Cost Crash Time Crash Cost Crash Cost

$/$

Day

$1$

$$

a

$4$

$$$

$5$

$0$

$2$

$$$

$1$

$5$

$0$

$($

$1$

$5$

$0$

$$

$5$

$0$

$)$

$/$

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