Question

1. Consider the network described in the table below.

Activity	Immediate Predecessor(s)	Pessimistic	Probable	Optimistic
J	--	15	10	8
K	--	9	8	7
L	J	10	6	5
M	J	3	3	3
N	K, M	9	5	1
O	K, M	10	7	4
P	L, N	10	8	3

Draw the network diagram and answer the following questions.

(a) Calculate the expected duration of each activity.

(b) Calculate the expected duration and variance of the critical path.

(c) Calculate the probability that the project will be completed in fewer than 30 time units.

Task	Early Start	Early Finish	Late Start	Late Finish	Slack	Mean	Variance
J	0
K	0
L
M
N
O
P
	Project					Project
						Std.dev

Answer 1

Below is the screenshot of the formula applied -

XUS 2020 - Excel FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Dynamics AX ? А e Define Name - Trace Precedents 15 Show Formulas Fx Use in Formula Trace Dependents Error Checking Insert AutoSum Recently Financial Logical Text Date & Lookup & Math & More Name Function Used Time Reference Trig Functions Manager Create from Selection Remove Arrows Remove Arrows - ft Evaluate Formula Function Library Defined Names Formula Auditing fx Σ Calculat GÒ Watch Window Calculation Calculat Options Calculation A1 : X Activity B C D E H - J L A Activity 1 IP a m b 2 - 8 10 15 3 K - 7 8 9 4 L J 5 6 10 F G K Expected Duration Variance ES EF LS LF Slack =(C2+4*D2+E2)/6 =((E2-C2)/6)^2 0 =H2+F2=K2-F2 =MIN(14:35) =K2-12 =(C3+4*D3+E3)/6 =((E3-C3)/6)^2 0 =H3+F3 =K3-F3 =MIN (J6:J7) =K3-13 =(C4+4*D4+E4)/6 =((E4-C4)/6)^2 =12 =H4+F4 =K4-F4 =8 =K4-14 =(C5+4*D5+E5)/6 =((E5-C5)/6)^2 =12 =H5+F5 =K5-F5 =MIN(J6:17) =K5-15 =(C6+4*D6+E6)/6 =((E6-C6)/6)^2 =MAX(13,15) =H6+F6 =K6-F6 =18 =K6-16 =(C7+4*D7+E7)/6 =((E7-C7)/6)^2 =MAX(13,15) =H7+F7 =K7-F7 =MAX(12:18) =K7-17 =(C8+4*D8+E8)/6 =((E8-C8)/6)^2 =MAX(14,16) =H8+F8 =K8-F8 =MAX(12:18) =K8-18 5 M J 3 3 3 6 1 9 N O KM KM L, N 5 17 7 4 10 8 P 3 8 10 9 10 Critical Path J-M-N-P 11 Project Expected Duration =F2+F5+F6+F8 12 Variance =G2+G5+G6+G8 13 SD =B12^(1/2) 14 P(X<30) =NORM.DIST(30,111,113,1)

Below is the screenshot of the result -

XUS 2020 - Excel FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Dynamics AX Trace Pre fx Σ Trace De Insert Function ? A e AutoSum Recently Financial Logical Text Date & Lookup & Math & More Used Time Reference Trigº Functions Function Library Name Manager Define Name Fx Use in Formula Create from Selection Defined Names Remove F20 : fic A B C D E H ski - J 1 Activity IP a m b 2 J 8 10 15 F G Expected Duration Variance 10.50 1.36 8.00 0.11 6.50 0.69 3.00 0.00 3 K 7 8 9 4 L 5 6 10 ES EF LS LF Slack 0.00 10.50 0.00 10.50 0.00 0.00 8.00 5.50 13.50 5.50 10.50 17.00 12.00 18.50 1.50 10.50 13.50 10.50 13.50 0.00 13.50 18.50 13.50 18.50 0.00 13.50 20.50 19.00 26.00 5.50 18.50 26.00 18.50 26.00 0.00 5 M J 3 3 3 6 N 1 5 9 5.00 1.78 7 0 KM KM L, N 4 7 10 1.00 7.00 7.50 8 P 3 8 10 1.36 J-M-N-P 26.00 9 10 Critical Path 11 Project Expected Duration 12 Variance 13 SD 14 P(X<30) 4.50 2.12 0.97033 15