Doug Casey is in charge of planning and coordinating next spring's sales manage$-$

ment training program for paying attendees. Doug has listed the following activity

information for this project.

assignment

$($a$)$ Draw a project network.

$($b$)$ Compute expected activity times and prepare an activity schedule, i$.$e$.$ determine

earliest and latest start and finish times.

$($c$)$ What are the critical activities and what is the expected project completion

time?

$($d$)$ If Doug wants a $0\mathrm{.}99$ probability of completing the project on time, how far ahead

of the scheduled meeting date should he begin working on the project?

$($e$)$ If the training program would be ready earlier, it could be advertised earlier

and there would be more paying attendees. Therefore, it is worth to invest in

crashing preparation times. By using the values of max. reduction times in

days and crash costs in $ per day and the fact that a week has $5$ working days,

formulate and write down a linear programme model that minimizes the cost to

crash the total project time by one week.

$($f$)$ Solve that linear program using the Simplex method in the online Management

Scientist package and report whether $1$ week acceleration is possible and if then

what the minimal cost for the speedup is$.$