in the table below. Your interest is in minimizing the cost of the project to the community center.

$\backslash$begin$\{$tabular$\}\{$cccccc$\}$

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

Normal $\backslash \backslash$

Time $($days$)$

$\backslash$end$\{$tabular$\}$ & Normal Cost $(\backslash$$$)$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Crash $\backslash \backslash$

Time $($days$)$

$\backslash$end$\{$tabular$\}$ & Crash Cost $(\backslash$$$)$ & Immediate Predecessor$($s$)\backslash \backslash$

$\backslash$hline START & $0$ & $0$ & $0$ & $0$ & $-\backslash \backslash$

A & $8$ & $50$ & $7$ & $170$ & START $\backslash \backslash$

B & $6$ & $40$ & $3$ & $280$ & START $\backslash \backslash$

C & $4$ & $70$ & $2$ & $290$ & B $\backslash \backslash$

D & $6$ & $20$ & $4$ & $100$ & A$,$ C $\backslash \backslash$

E & $5$ & $30$ & $5$ & $30$ & A$,$ C $\backslash \backslash$

F & $7$ & $80$ & $3$ & $600$ & B $\backslash \backslash$

G & $10$ & $50$ & $7$ & $350$ & D $\backslash \backslash$

H & $10$ & $60$ & $9$ & $90$ & E$,$ F $\backslash \backslash$

FINISH & $0$ & $0$ & $0$ & $0$ & G$,$ H $\backslash \backslash$

$\backslash$hline

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

a$.$ Using the normal times for each activity, what is the earliest date you can complete the project?

The corresponding project duration using the normal times is $26$ days. $($Enter your response as an integer.$)$

b$.$ Suppose the variable overhead costs are $\backslash (\backslash$$ $40\backslash )$ per day for your project. Also, suppose that the center must pay $\backslash (\backslash$$ $70\backslash )$ per day for a temporary room on day $17$ or beyond. Find the minimum$-$cost project schedule.

Fill in the table below to show the proper schedule $($time for each activity after crashing$)$ for completing the project at minimum cost. $($Enter your responses as integers.$)$

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

$\backslash$hline Activity & Time $($days$)$ & Activity & Time $($days$)\backslash \backslash$

$\backslash$hline A & $\backslash (\backslash$square $\backslash )$ & E & $\backslash (\backslash$square $\backslash )\backslash \backslash$

B & $\backslash (\backslash$square $\backslash )$ & F & $\backslash (\backslash$square $\backslash )\backslash \backslash$

C & $\backslash (\backslash$square $\backslash )$ & G & $\backslash (\backslash$square $\backslash )\backslash \backslash$

D & $\backslash (\backslash$square $\backslash )$ & H & $\backslash (\backslash$square $\backslash )\backslash \backslash$

$\backslash$hline

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