We want to $*$somehow$*$ decrease the answer to part g$)$ the probability of being late and the answer to part h$)$ the $95\%$ certainty time.$$ Assume you can crash any of the activities above at the costs and limits listed in problem $2)$ you might notice the optimistic times are the same as the crash times.$$ Ignore the possibility of saving by slowing down and assume that you can only crash activities by integer amounts.$$ If you crash an activity by one day, the optimistic time stays the same, the most likely time decreases by $1$ day and the pessimistic time decreases by $1\mathrm{.}5$ days.$$ So$,$ for $$850$ you could change activity A from $(4,7,16)$ to $(4,6,14\mathrm{.}5).$ For $2*$$$850=$ $$1700,$ you could change activity A from $(4,7,16)$ to $(4,5,13).$

a$)$ At minimum cost, which activities should you crash, and by how much, in order to cut the probability of being late in half?$($How do you cut the answer to part g$)$ in half at minimum cost?$)$

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b$)$ At minimum cost, which activities should you crash, and by how much, in order to decrease the $95\%$ certainty time down to $36$ days?$($How do you get the answer to part h$)$ down to $36$ at minimum cost?$)\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$r$|$r$|$r$|\}$

$\backslash$hline Act & I.P$.$ & $\backslash$multicolumn$\{1\}\{$l$|\}\{$ Opt $\}$ & $\backslash$multicolumn$\{1\}\{$l$|\}\{$ ML $\}$ & Pess & Mean & SD $\backslash \backslash$

$\backslash$hline A & $---$ & $\backslash (\backslash$mathbf$\{4\}\backslash )$ & $7$ & $16$ & $8\mathrm{.}0$ & $2\mathrm{.}0\backslash \backslash$

$\backslash$hline B & $---$ & $1$ & $2$ & $7$ & $2\mathrm{.}7$ & $1\mathrm{.}0\backslash \backslash$

$\backslash$hline C & $---$ & $6$ & $11$ & $18$ & $11\mathrm{.}3$ & $2\mathrm{.}0\backslash \backslash$

$\backslash$hline D & A & $5$ & $\backslash (\backslash$mathbf$\{8\}\backslash )$ & $25$ & $10\mathrm{.}3$ & $3\mathrm{.}3\backslash \backslash$

$\backslash$hline E & A & $5$ & $8$ & $10$ & $7\mathrm{.}8$ & $0\mathrm{.}8\backslash \backslash$

$\backslash$hline F & B & $7$ & $9$ & $21$ & $10\mathrm{.}7$ & $2\mathrm{.}3\backslash \backslash$

$\backslash$hline G & C & $10$ & $16$ & $28$ & $17\mathrm{.}0$ & $3\mathrm{.}0\backslash \backslash$

$\backslash$hline H & D & $3$ & $4$ & $8$ & $4\mathrm{.}5$ & $0\mathrm{.}8\backslash \backslash$

$\backslash$hline I & E$,$ F & $\backslash (\backslash$mathbf$\{2\}\backslash )$ & $5$ & $10$ & $5\mathrm{.}3$ & $1\mathrm{.}3\backslash \backslash$

$\backslash$hline J & H$,$ I & $5$ & $10$ & $20$ & $10\mathrm{.}8$ & $2\mathrm{.}5\backslash \backslash$

$\backslash$hline

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