$8.$ Consider the following situation:

$$Let$$s plan a graduation party for our seniors,$$ suggested Jim, president of the fraternity. Everyone on the fraternity council thought that it was a good idea, so they agreed to brainstorm ideas for the party.

$$First$,$ we have to pick a date,$$ suggested Joe. $$It$$ll have to be after final exams are over, but before graduation.$$

$$That narrows it down pretty quickly to June $8,9,$ or $10.$ The $11$th is a Sunday and the $12$th is graduation day,$$ said Jim. $$I propose that we try for Thursday the $8$th$,$ with the alternate date of Friday, the $9$th$.$ We$$ll have to take a vote at the fraternity meeting tomorrow.$$

$$Now$,$ let$$s list things that have to be done in order to get ready for the party,$$ suggested Amber. They quickly produced the following list $($not in any order$)$:

$$ Pick date

$$ Plan menu

$$ Get food delivered

$$ Estimate costs

$$ Locate and book a hall

$$ Determine budget

$$ Select music

$$ Hire a DJ

$$ Plan decorations

$$ Setup, decorate hall

$$ Determine how much can be paid from treasury and what the cost of the special assessment will be for each member

$$ Design and print invitations

$$ Set up mailing list

$$ Dress rehearsal $($day before party$)$dummy activity$$

$$ Mail invitations

$$ Plan ceremony for seniors

$$ Rehearse ceremony

$$ Plan after$-$party cleanup and bill paying

$$ Have the party

$$ Cleanup and pay bills

Next, they selected Joe to lead the planning because he had fraternity party planning experience. Put yourself in Joe$$s position and develop a comprehensive plan for the party. Here$$s a suggested approach:

a$)$ Use your judgment to estimate the duration of each activity and organize the estimates in a table. $(5$ Points$)$

b$)$ Develop a precedence diagram $($network$)$ for the $20$ party preparation activities listed above. Use your judgment again to assign precedence relationships between the activities in the network. $(10$ Points$)$

c$)$ Develop and visualize a schedule to be used by the party planners for planning and monitoring the progress of the party preparation. Visualize the schedule using a Gantt chart. $(5$ Points$)$

d$)$ Estimate how long the party preparation will take. $(5$ Points$)$