Alfred Lowenstein is the president of the research division for Better Health, Inc., a major pharmaceutical company. His most important project coming up is the development of a new drug to combat AIDS. He has identified 10 groups in his division which will need to carry out different phases of this research and development project. Referring to the work to be done by the respective groups as activities A, B, . . . , J, the precedence relationships for when these groups need to do their work are shown in the following project network.

To beat the competition, Better Health€™s CEO has informed Alfred that he wants the drug ready within 22 months if possible.
Alfred knows very well that there is considerable uncertainty about how long each group will need to do its work. Using the PERT three-estimate approach, the manager of each group has provided a most likely estimate, an optimistic estimate, and a pessimistic estimate of the duration of that group€™s activity. Using PERT formulas, these estimates now have been converted into estimates of the mean and variance of the probability distribution of the duration of each group€™s activity, as given in the following table (after rounding to the nearest integer).

(a) Find the mean critical path for this project.
(b) Use this mean critical path to find the approximate probability that the project will be completed within 22 months.
(c) Now consider the other three paths through this project network. For each of these paths, find the approximate probability that the path will be completed within 22 months.
(d) What should Alfred tell his CEO about the likelihood that the drug will be ready within 22 months?

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START FINISH Duration Activity Estiinated Mean Estimated Variance 4 months 6 months 4 months 3 months 8 months 4 months 3 months 7 months 5 months 5 months 5 months 10 months 8 months 6 months 12 months 6 months 5 months 14 months 8 months 7 months