PROBLEM $3[$HW$2]$

Fusion Engineering Inc. is designing a new product for welding two different alloys. The company has limited time and resources to complete the project. The following activity information is available.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Activity & $\backslash$begin$\{$tabular$\}\{$c$\}$

Immediate $\backslash \backslash$

Predecessor$($s$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Normal $\backslash \backslash$

Time $\backslash \backslash$

$($Days$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Normal $\backslash \backslash$

Cost $(\backslash$$$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Crash $\backslash \backslash$

Cost$/$Day $(\backslash$$$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Crash Time $\backslash \backslash$

$($Days$)$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline A & $-$ & $4$ & $400$ & $125$ & $3\backslash \backslash$

$\backslash$hline B & A & $5$ & $800$ & $200$ & $4\backslash \backslash$

$\backslash$hline C & A & $4$ & $520$ & $150$ & $2\backslash \backslash$

$\backslash$hline D & B & $3$ & $600$ & $225$ & $2\backslash \backslash$

$\backslash$hline E & C & $3$ & $255$ & $100$ & $2\backslash \backslash$

$\backslash$hline F & B$,$ E & $4$ & $600$ & $175$ & $2\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$)$ Draw the project network.

b$)$ Find critical path.

c$)$ Find the project completion time and the corresponding cost.

d$)$ What is the total cost, if the project deadline is $13$ days?

e$)$ Assume the project deadline to be $10$ days. The company has to bear $\backslash (\backslash$$ $170\backslash )$ for each day of delay. Find the optimal number of days to crash the project.