For the problem given in Exercise 4.12, assuming that the variance of duration is 0 for all the project phases, determine the time-cost trade-off curve by defining the strategies and calculating crashing cost for each strategy for \(T_{\max } \leq T \leq T_{\min }\).

Exercise 4.12

Answer the following questions using the tabulated project data.

a. There is a penalty of $3,000/day beyond the normal PERT duration. Perform a crashing analysis to compare total normal cost to total crash cost. First crash only the critical activities; then crash all activities.

b. Find the probability that the total lateness penalty will be less than $3,000.

c. Find the probability that the total lateness penalty will be $3,000 or less.

d. Find the probability that the total lateness penalty will be greater than $3,000.

e. Find the probability that the total lateness penalty will be less than $9,000.

Project Preceding Normal Normal Crash Crash Variance of Phase Phase Time Cost Time Cost Duration A 40 $9,000 30 $12,000 10 B C AA 53 15,000 50 15,300 9 60 7,500 30 6,000 600 D A 35 20,000 30 22,000 25 E C, D 28 12,000 20 15,000 40 F B, E 30 6,000 27 7,000 30