Southwestern University $($SWU$),$ a large state college in Stephenville, Texas, $30$ miles southwest of the Dallas$/$Fort Worth metroplex, enrolls close to $20,000$ students. In a typical town$-$gown relationship, the school is a dominant force in the small city, with more students during fall and spring than permanent residents.

A longtime football powerhouse, SWU is a member of the Big Eleven conference and is usually in the top $20$ in college football rankings. To bolster its chances of reaching the elusive and long$-$desired number$-$one ranking, in $2012,$ SWU hired the legendary Phil Flamm as its head coach.

One of Flamm's demands on joining SWU had been a new stadium. With attendance increasing, SWU administrators began to face the issue head$-$on$.$ After $6$ months of study, much political arm wrestling, and some serious financial analysis, Dr$.$ Joel Wisner, president of Southwestern University, had reached a decision to expand the capacity at its on$-$campus stadium.

Adding thousands of seats, including dozens of luxury skyboxes, would not please everyone. The influential Flamm had argued the need for a first$-$class stadium, one with built$-$in dormitory rooms for his players and a palatial office appropriate for the coach of a future NCAA champion team. But the decision was made, and everyone, including the coach, would learn to live with it$.$

The job now was to get construction going immediately after the $2019$ season ended. This would allow exactly $270$ days until the $2020$ season opening game. The contractor, Jefferson Construction, signed his contract. Malick Jefferson looked at the tasks his engineers had outlined and looked President Wisner in the eye. "I guarantee the team will be able to take the field on schedule next year," he said with a sense of confidence. "I sure hope so$,"$ replied Wisner. "The contract penalty of $$10,000$ per day for running late is nothing compared to what Coach Flamm will do to you if our opening game with Penn State is delayed or canceled." Jefferson, sweating slightly, did not need to respond. In football$-$crazy Texas, Jefferson Construction would be mud if

the $270-$day target was missed.

Back in his office, Jefferson again reviewed the data $($see the following table$)$ and noted that optimistic time estimates can be used as crash times. He then gathered his supervisors. "Folks, if we're not $75\%$ sure we'll finish this stadium in less than $270$ days, I want this project crashed! Give me the cost figures for a target date of $250$ days$$also for $240$ days. I want to be early, not just on time!"

Time Estimates $($Days$)$

Activity Description Predecessor$($s$)$ Optimistic Most Likely Pessimistic Crash Cost$/$Day

A Bonding, insurance, tax structuring $203040$ $$1,500$

B Foundation, concrete footings for boxes A $2065803,500$

C Upgrading skybox stadium seating A $50601004,000$

D Upgrading walkways, stairwells, elevators C $30501001,900$

E Interior wiring, lathes B $2530359,500$

F Inspection approvals E $0\mathrm{.}10\mathrm{.}10\mathrm{.}10$

G Plumbing D$,$ F $2530352,500$

H Painting G $1020302,000$

I Hardware$/$AC$/$metal workings H $2025602,000$

J Tile$/$carpet$/$windows H $810126,000$

K Inspection J $0\mathrm{.}10\mathrm{.}10\mathrm{.}10$

L Final detail work$/$cleanup I, K $2025604,500$

Answer the following questions here and show your detailed work $($solution$)$ below for each part starting next page. If you worked on a spreadsheet, copy it under each part of your solution. Once finished, create a pdf file, and upload it on Blackboard. Answer the questions on MyLab.

Part $1$: What is the length of the critical path as computed from the table?

$[$Your answer here$]$

Part $2$: What is the standard deviation of the critical path?

Part $3$: What is the probability of completing the project in $270$ days?

Part $4$: What is the cost of crashing to $250$ days?