TechVision Solutions is a forward$-$thinking startup on a mission to revolutionize urban mobility. Their latest endeavor is developing a state$-$of$-$the$-$art autonomous drone delivery system. To ensure timely completion of this system, they need your team's help to employ project scheduling, PERT, and crashing techniques.

The table below was generated after surveying the experts in the field, and includes the activities' times $($days$),$ predecessors, costs $($USD$),$ as well as the crash times.

The project should be completed within $30$ days, after which the opportunity costs of losing customers are estimated at $$4,000$ for every additional day.

$\backslash$table$[[$Activity$,$Predecessor$($s$),$Optimistic,Most Likely,Pessimistie,Normal Cost,CrashTime,Crash Cost$],[$A$,,8,11,20,12000,8,13080],[$B$,,6,14,16,10800,7,18000],[$C$,$A$,8,10,30,8880,4,12120],[$D$,$C$,2,6,16,14400,3,20000],[$E$,$B$,$C$,2,3,4,9600,2,20160],[$F$,$D$,$E$,$I,N$,5,5,23,13200,5,16080],[$G$,,1,1,13,15360,1,32640],[$H$,,1,2,3,10800,1,18720],[$I$,$G$,$H$,14,20,38,8280,14,15480],[$J$,,2,4,6,16560,2,18120],[$K$,,3,5,7,12000,3,29760],[$L$,,6,7,8,10800,6,14400],[$M$,$K$,$L$,1,4,7,8880,1,21480],[$N$,$J$,$M$,12,15,18,11520,12,16920]]$

Case Report

Perform an analysis of the project and prepare a report presenting your findings and recommendations. Include $($but do not limit your discussion to$)$ a consideration of the following items.

Determine the critical path. How long is the project expected to take?

What is the probability for the completion to take longer than $30$ days?

Due to the importance of this system, TechVision wants to be at least $60\%$ confident that the completion will be done in $30$ days. Accordingly, crash the project as needed, in order to achieve this target. Report the budget you will need to cover the crashing costs.

Hint: Your crashing costs cannot be more than the opportunity costs.