$3\mathrm{.}20$ Development of Version $2\mathrm{.}0$ of a particular accounting software product is being considered by Jose Noguera's technology firm in Baton Rouge. The activities necessary for the completion of this project are listed in the following table:

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

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

NORMAL $\backslash \backslash$

TIME $\backslash \backslash$

$($WEESS$)$

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

CRASH $\backslash \backslash$

TIME $\backslash \backslash$

$($WEEKS$)$

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

NORMAL $\backslash \backslash$

COST

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

CRASH $\backslash \backslash$

COST

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

IMMEDIATE $\backslash \backslash$

PREDECESSOR$($S$)$

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

$\backslash$hline ACTIVITY & $4$ & $3$ & $\backslash (\backslash$$ $2,000\backslash )$ & $\backslash (\backslash$$ $2,600\backslash )$ & $-\backslash \backslash$

$\backslash$hline B & $2$ & $1$ & $2,200$ & $2,800$ & $-\backslash \backslash$

$\backslash$hline C & $3$ & $3$ & $500$ & $500$ & $-\backslash \backslash$

$\backslash$hline D & $8$ & $4$ & $2,300$ & $2,600$ & A $\backslash \backslash$

$\backslash$hline E & $6$ & $3$ & $900$ & $1,200$ & B $\backslash \backslash$

$\backslash$hline F & $3$ & $2$ & $3,000$ & $4,200$ & C $\backslash \backslash$

$\backslash$hline G & $4$ & $2$ & $1,400$ & $2,000$ & D$,$ E $\backslash \backslash$

$\backslash$hline

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

a$)$ What is the project completion date?

b$)$ What is the total cost required for completing this project on normal time?

c$)$ If you wish to reduce the time required to complete this project by $1$ week, which activity should be crashed, and how much will this increase the total cost?

d$)$ What is the maximum time that can be crashed? How much would costs increase?