Chapter 21, Problem 1DP

Q1: By using the PERT technique, the durations of the activities were calculated as shown in the table below, Draw an activity network for project by using Activity On Node (AON) method and find: 1. The project's total duration and date of completion and CP (assume the project start date is the 1st of June 2025)? 2. The overall variance of the project? 3. The probability of completing the project in 30 days? 4. The probability of completing the project in 22th of June 2025? 5. With a probability of 75%, what is the expected duration and date for completing the project? Activity Preceding activity K Optimistic duration (day) 4 Most likely duration (day) Pessimistic duration (day) 5 12 L 5 M K 5 11 8 17 11 N K 3 4 11 0 L 2 3 10 P M,N 4 7 10 Q N 3 7 17 R N,O 6 9 18 S P,Q,R 1 3 5

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Q2: For the activities shown in the table below, it is required to reduce the total duration of the project four days by using crash program and network diagram, If you knew that indirect costs is 150 S/day and the delay fine is 100 $/day after the 14th day. Find new cost after crashing the project four days? Activity Preceding Normal Program Crash Program activity Duration (days) Direct Cost (S) Duration (days) Direct Cost (S) A 5 600 3 950 B - 4 200 3 500 C A 5 300 4 500 D A 2 600 1 615 E B 6 900 5 1025 800 3 F C 4 700 450 G D 4 400 3 700 3 700 1400 3 H E 2 600 I F,G,H 4 5000 Σ (40 px) good luck)

I need detailed help solving this exercise from homework of Engineering Mathematics II.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!

Determine the stiffness matrix of the frame as shown in Fig. 4. Nodes 1 and 3 are fixed supports. Assume I = 300(10^6) mm4, A = 10(10^3) mm2, E = 200 GPa for each member. Indicate the degrees-of freedom in all the stiffness matrices. Use the values of L3=2.5m, L4=4.5m, w=12kN/m and P=10kN.  Please show all working and explain how the code numbers for global matrix are determined in detail.

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I need detailed help solving this exercise from homework of Engineering Mathematics II.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!

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