PROBLEM

A project has a sequence of $10$ activities with the following characteristics:

$\backslash$table$[[,,$Time Estimate in Weeks$],[$Activity$,\backslash$table$[[$Preceding$],[$activity$]],\backslash$table$[[$Carla$\text{'}$s$],[$Estimate $($Ta$)]],\backslash$table$[[$Tim$\text{'}$s Estimate$],[($Tb$)]]],[$A$,-,4,5],[$B$,-,1,1\mathrm{.}5],[$C$,$A$,2,3],[$D$,$A$,3,4],[$E$,$A$,2,3],[$F$,$C$,1\mathrm{.}5,2],[$G$,$D$,1\mathrm{.}5,3],[$H$,$B$,$ E$,2\mathrm{.}5,3\mathrm{.}5],[$I$,$H$,1\mathrm{.}5,2],[$J$,$F$,$ G$,$ I,$1,2]]$

Two people, Carla and Tim have prepared the estimate of the time for each task and have presented their inputs in Estimate$-1$ and Estimate$-2,$ respectively.

$($a$)$ Using the above table, determine the least amount of time needed to complete the project as per Carla's and Tim's respective estimates. In doing so$,$ identify the critical tasks in achieving these times as per Carla's data and Tim's data. Compare their times and determine whose estimated time is shorter.

$($b$)$ As a manager, you give these estimates to your specialist, Martha. She suggests using the following formula to determine the estimated time for each task:

$T_c=\frac{1\mathrm{.}5T_a+1\mathrm{.}4T_b+0\mathrm{.}1}{3}$

Prepare a third column with the above formula for each task and then determine the least amount of time needed to complete the project and the critical tasks$/$path as per Martha. Finally, compare the times predicted by Carla's, Tim's and Martha's estimates and determine the shortest time and the l

PROBLEM

A project has a sequence of $10$ activities with the following characteristics:

$\backslash$table$[[,,$Time Estimate in Weeks$],[$Activity$,\backslash$table$[[$Preceding$],[$activity$]],\backslash$table$[[$Carla$\text{'}$s$],[$Estimate $($Ta$)]],\backslash$table$[[$Tim$\text{'}$s Estimate$],[($Tb$)]]],[$A$,-,4,5],[$B$,-,1,1\mathrm{.}5],[$C$,$A$,2,3],[$D$,$A$,3,4],[$E$,$A$,2,3],[$F$,$C$,1\mathrm{.}5,2],[$G$,$D$,1\mathrm{.}5,3],[$H$,$B$,$ E$,2\mathrm{.}5,3\mathrm{.}5],[$I$,$H$,1\mathrm{.}5,2],[$J$,$F$,$ G$,$ I,$1,2]]$

Two people, Carla and Tim have prepared the estimate of the time for each task and have presented their inputs in Estimate$-1$ and Estimate$-2,$ respectively.

$($a$)$ Using the above table, determine the least amount of time needed to complete the project as per Carla's and Tim's respective estimates. In doing so$,$ identify the critical tasks in achieving these times as per Carla's data and Tim's data. Compare their times and determine whose estimated time is shorter.

$($b$)$ As a manager, you give these estimates to your specialist, Martha. She suggests using the following formula to determine the estimated time for each task:

$T_c=\frac{1\mathrm{.}5T_a+1\mathrm{.}4T_b+0\mathrm{.}1}{3}$

Prepare a third column with the above formula for each task and then determine the least amount of time needed to complete the project and the critical tasks$/$path as per Martha. Finally, compare the times predicted by Carla's, Tim's and Martha's estimates and determine the shortest time and the largest time needed.

Criteria to pass the project:

For each part of the question

The PERT analysis diagram is clearly drawn

The estimates are clearly indicated

The calculations are correcta

Criteria to pass the project:

For each part of the question

The PERT analysis diagram is clearly drawn

The estimates are clearly indicated

The calculations are correct