Please type in doc or hand-write the working steps on paper for each problem. WRITE LEGIBLY. please show the working steps. There are 4 questions with sub-sections.The precedence chart is given...

1
    Part 1, 2 and 3
    Activity    Optimistic Time (days)    Most Likely time (days)    Pessimistic Time (days)    Expected Time     Task Variance
    A    4    8    12    8    1.7777777778
    B    2    3    4    3    0.1111111111
    C    5    10    15    10    2.7777777778
    D    3    5    7    5    0.4444444444
    E    4    6    8    6    0.4444444444
    F    2    4    6    4    0.4444444444
    The network diagram would be
    The critical path of the project is A-C-D-E
    The Expected Time (Te) of the project is 29 days
    The critical path of the project contains all those tasks with Total Slack (TS) equal to zero (0).
    Part 4:
    To calculate probabilities, we use the Z-Score formula:
    σ = √1.7778 + 2.7778 + 0.4444 + 0.4444
    
σ = √5.4444
    
σ = 2.3333
    Thus,
    Z-Score = (32 - 29) / 2.3333
    Z-Score = 3 / 2.3333
    Z-Score = 1.2857
1.29
    Hence, according to the Z-Score table, if the Z-Score is 1.29, the probability to complete the project within 32 days is 0.9015
90.15%.
2
    According to the information in the exercise, the network diagram:
    The original duration of the project is 12 days. The critical path of the project contains all the tasks with slack equal to zero (0). The original critical path of the project is A-C.
    Smoothing implies distributing the resources throughout the duration of the project avoiding extending it as much as possible.
3
    Activity    Immediate
Predecessors    Normal Time
(days)     Crash Time
(days)    Normal Cost
$    Crash Cost
$    Crash Period
available    Cost
per day
    A    -    4    2    $200.00    $500.00    2    150
    B    -    3    3    $300.00    $300.00    0    0
    C    A,B    6    2    $800.00    $1,200.00    4    100
    D    -    4    3    $400.00    $600.00    1    200
    F    D    8    5    $1,000.00    $1,600.00    3    200
    Normal CPM Network                                After crashing for 5-days
        Initially                Run -1            Run -2            Run -3            Run -4            Run -5
    Activity    Normal Duration    Crash Duration    cost/day    TF    Days Saved    Dur    TF    Days Saved    Dur    TF    Days Saved    Dur    TF    Days Saved    Dur    TF    Days Saved    Dur    TF
    A    4    2    150    2        4    1        4    0        4    1        4    1        4    1
    B    3    3    0    3        3    2        3    1        3    2        3    2        3    2
    C    6    2    100    2        6    1        6    0    1    5    1        5    1    1    4    1
    D    4    3    200    0    1    3    0        3    0        3    0        3    0        3    0
    F    8    5    200    0        8    0    1    7    0        7    0    1    6    0        6    0
    Cost                        200            200            100            200            100
    Savings                        0            0            0            0            0
    project cost            $2,700.00            $2,500.00            $2,300.00            $2,200.00            $2,000.00            $1,900.00
    project duration            12    days        11            10            10            9            9
    Extra Cost            $800.00
4
    Project Duration (in months)    % of projects                Simulation    Outcome
    10    35.00                1    27.5296159107
    12    30.00                2    -4.9207402005
    14    15.00                3    26.630963409
    18    20.00                4    15.2850293949
                        5    23.5803847574
    Mean    25.00                6    23.6279441214
    Standard Deviation    9.1287092918                7    13.8907344594
                        8    23.1749139937
    27.5296159107                    9    21.9568497218
                        10    20.1565372027
                        11    18.5308125213
    Solution                    12    19.1082284439
    Random Numbers for Project    Project...