$|$Problem $1$: $(30)$

Given:

EarthWorks, Inc. is a general contractor specializing in site clearing, underground utilities, paving, and truf. The company was just awarded a new project, to prepare a $50-$acre site for a new shopping mall. As Construction Manager for EarthWorks, you are tasked with developing a schedule and the owner is concerned that the project might take longer than originally planned. A list of tasks, immediate predecessors, and probable activity durations are provided in the table below.

$\backslash$table$[[$Activity$,$Predecessor,$\backslash$table$[[$Budget$],[($$K$)]],\backslash$table$[[$Optimistic$],[$Duration$],[($weeks$)],[$a$]],\backslash$table$[[$Most$],[$probable$],[$Duration$],[($weeks$)],[$m$]],\backslash$table$[[$Pestimistic$],[$Duration$],[($weeks$)],[$b$]]],[$A$)$ Planning & Permitting,Start,$$10,0\mathrm{.}5,2\mathrm{.}0,3\mathrm{.}0],[$B$)$ Mobilize$/$Temp$.$ Utilities,A$,$$$30,0\mathrm{.}5,1\mathrm{.}0,2\mathrm{.}0],[$C$)$ Site Survey,A$,$$$50,2\mathrm{.}0,3\mathrm{.}0,3\mathrm{.}5],[$D$)$ Site Clearing,B$,$C$,$$$500,5\mathrm{.}0,6\mathrm{.}0,8\mathrm{.}0],[$E$)$ Rough Grading,B$,$C$,$$$375,2\mathrm{.}5,3,4\mathrm{.}0],[$F$)$ Undergroung Utilities,B$,$C$,$$$3,000,4\mathrm{.}0,5,8\mathrm{.}0],[$G$)$ Finish Grading,D$,$E$,$F$,$$$200,1\mathrm{.}5,2,3\mathrm{.}0],[$H$)$ Base Course,G$,$$$1,500,1\mathrm{.}5,2,3\mathrm{.}0],[$I$)$ Asphalt Paving,H$,$$$2,500,2\mathrm{.}5,3,6\mathrm{.}0],[$J$.)$Loam & Seed,I,$$250,1\mathrm{.}5,2,4\mathrm{.}0],[$Total Budget $=,$$$8,415,,,]]$

Find: $($Show all calculations$)$

Project schedule network diagram. $(5)$

Expected project duration. $(5)$

Probability that the project will take longer than $22$ weeks. $(5)$

Using Expected ES and EF and budget of each activity develop a Project Budget Baseline Curve for the project $(10)$

What is your prediction of project duration with less than $10\%$ risk of exceedance. $(5)$