Exhibit $1$

PROJECT DESCRIPTION AND TIME ESTIMATES $($WEEKS$)$

$\backslash$table$[[$Task$,\backslash$table$[[$Description$],[$optimistic$]],\backslash$table$[[$Most$],[$likely$]],\backslash$table$[[$Most$],[$pessimistic$]],$IP$,],[$A$,$Requirements,$3,4,6,$None$],[$B$,$Market assessment,$4,7,10,$A$],[$C$,$Design,$5,6,9,$A$],[$D$,$Development,$6,7,16,$C$],[$E$,$Testing,$7,9,10,$D$],[$F$,$Revising,$4,5,6,$B$,$ E$],[$G$,$Documentation,$3,6,10,$D$],[$H$,$Quality assurance,$3,5,7,$C$,$ E$],[$I$,$Pricing,$2,2,2,$B$],[$J$,$Production,$3,4,14,$F$,$ G$,$ H$,$ I$],[$K$,$Distribution,$2,3,4,$J$]]$

Exhibit $2$

PROJECT CRASH DATA

$\backslash$table$[[$Task$,$Normal costs $($$$),$Crash time $($weeks$),$Crash costs $($$$)],[$A$,10,000,3,10,000],[$B$,20,000,6,25,000],[$C$,15,000,5,30,000],[$D$,45,000,6,65,000],[$E$,10,000,8,20,000],[$F$,15,000,4,18,000],[$G$,20,000,4,30,000],[$H$,10,000,3,15,000],[$I$,5,000,2,5,000],[$J$,40,000,5,50,000],[$K$,15,000,2,25,000]]1.$ Draw the project network diagram and calculate the following: ES$,$ EF$,$ LS$,$ LF$,$ total slack, free slack, and safety slack.

$2.$ What is the estimated completion time for this project? What is the estimated project budget? What is the probability that the project can be completed in $35$ weeks?

$3.$ Assume that partial crashing is allowed. What is the minimum expected time in which the project can be completed? What is the probability of completing the project in this time?

$4.$ What is the additional cost for reducing the project time to the required $35$ weeks? Which specific tasks do you recommend crashing in order to achieve this milestone?

$5.$ What is the impact on the crashing solution if the expected time for task B is increased from $7$ weeks to $9$ weeks? Explain with supporting evidence.

$6.$ What is the impact on the crashing solution if the expected time for task H is decreased to $3$ weeks? What if the expected time for task E is decreased to $8$ weeks? Explain with supporting evidence.