$($c$)[10]$ The project is ready to begin now, and the deadline for completion is $100$ weeks. What duration should the project manager plan for in order to have a $95\%$ likelihood of completing the project by the deadline? Note: If this planning date is less than the expected project duration, you may assume that activities may be crashed $($e$.$g$.$ durations reduced$)$ with no change in the activity variance.

ANSWER: $0\mathrm{.}95=P_{t_{p_{-}}}100=(1\mathrm{.}65)=(\frac{(100-t_p)}{\sqrt[\phantom{2}]{{\displaystyle \underset{?}{\overset{?}{}}}{}_e^2}})=(\frac{(100-t_p)}{\sqrt[\phantom{2}]{{1\mathrm{.}67}^2+{5\mathrm{.}67}^2+3^2}})$

$1\mathrm{.}65=\frac{(100-t_p)}{\sqrt[\phantom{2}]{{1\mathrm{.}67}^2+{5\mathrm{.}67}^2+3^2}}=>t_p=(-1\mathrm{.}65**6\mathrm{.}625)+100=89\mathrm{.}1$ weeks

Dr$.$ L$.$ Dale Thomas

April $4,2024$