A certain company is planning to run a project whose activities are summarized in the table below.

Task ID

Description

Immediate Predecessor

Duration $($months$)$

$1$

Install New Software Package

$2$

Assess Requirements

$3$

Assess Requirements

$--$

$1\mathrm{.}0$

$4$

Design

$5$

Design Business System

$3$

$2\mathrm{.}5$

$6$

Develop

$7$

Modify Purchased Package

$5$

$2\mathrm{.}0$

$8$

Modify$-$In$-$House Procedures

$5$

$1\mathrm{.}5$

$9$

Modify Manual Systems Flow

$5$

$4\mathrm{.}0$

$10$

Test

$11$

Test Purchased Package

$7$

$1\mathrm{.}5$

$12$

Test In$-$House Procedures

$8$

$1\mathrm{.}0$

$13$

Test Manual Systems Flow

$9$

$1\mathrm{.}0$

$14$

Implement

$15$

Implement New Software Package

$11,12,13$

$1\mathrm{.}5$

$16$

Train Staff

$11,12,13$

$0\mathrm{.}5$

a$)$ How many months will it take to complete the project?

b$)$ Which activities are critical?

c$)$ What is the total slack for each of the activities that are not critical?

d$)$ If the project were started on June $3,2024,$ and observed all the US Legal holidays, on what day will the project be completed?