Q$3$: Lesson $3$: $[$CLR $3](20$ marks$)$

Springboard Inc. manufactures diving boards for both residential and commercial $/$ public pools. They have received notice from their landlord that due to improper installation of the building$$s vapour barrier, there is dangerous mold growing behind the walls and the building has to be evacuated. The timing could not be worse for Springboard as they are in the middle of maximum production getting product out for the summer season. There is a large order placed by a hotel chain that is due in $2$ weeks. The president of Springboard wants the operations manager to let her know if she should call the hotel chain to let them know that the deliver may be delayed. She also realizes she risks losing the order but would rather be up front with the hotel chain rather than surprising them at the last moment with a late deliver. The operations manager, William, begins working out the details of moving production to a new facility. He knows that a number of activities will have to occur and some activities must be completed before others can begin. Each activity also has a duration.

He completes the following Activity Chart:

a$)$ Create an Activity on Node $($AON$)$ project network associated with the activities on William$$s activity chart. $(3$ marks$)$

b$)$ Determine the critical path and the time it will take to complete the project.

$(7$ marks$)$

c$)$ William would like to be able to tell the president that Operations will be able to move the facility to a new location, set up$,$ produce, and ship the hotel chain$$s order within two weeks, but he needs some reassurance. To do this, he calculates an optimistic and pessimistic time for each activity as follows:

Using the data from William regarding optimistic, most likely, and pessimistic times for each activity, calculate the total expected time using the beta distribution weighting. What should William tell the President? You must show your work and any formulas used to arrive at your answer. $(2$ marks$)$

d$)$ William wants to be as confident as he can about projecting the time it will take to complete the project. What is the probability that William$$s Operations Department will ship the product to the hotel chain within $14$ days? $(5$ marks$)$

e$)$ William does not want to cut the project too close to the date the hotel chain is expecting to receive their product. He thinks he should add more resources, such as labour and suppliers, to increase the probability of shipping the boards on time. He creates the following chart to show the cost of $$crashing$$ various activities

Which activities should William crash to complete the project $2$ days earlier than projected? You must show your work to validate the activities you recommend to be crashed. $(3$ marks$)$