# Question

Sharon Lowe, vice president for marketing for the Electronic Toys Company, is about to begin a project to design an advertising campaign for a new line of toys. She wants the project completed within 57 days in time to launch the advertising campaign at the beginning of the Christmas season.

Sharon has identified the six activities (labeled A, B, . . . , F) needed to execute this project. Considering the order in which these activities need to occur, she also has constructed the following project network.

Using the PERT three-estimate approach, Sharon has obtained the following estimates of the duration of each activity.

(a) Find the estimate of the mean and variance of the duration of each activity.

(b) Find the mean critical path.

(c) Use the mean critical path to find the approximate probability that the advertising campaign will be ready to launch within 57 days.

(d) Now consider the other path through the project network. Find the approximate probability that this path will be completed within 57 days.

(e) Since these paths do not overlap, a better estimate of the probability that the project will finish within 57 days can be obtained as follows. The project will finish within 57 days if both paths are completed within 57 days. Therefore, the approximate probability that the project will finish within 57 days is the product of the probabilities found in parts (c) and (d). Perform this calculation. What does this answer say about the accuracy of the standard procedure used in part (c)?

Sharon has identified the six activities (labeled A, B, . . . , F) needed to execute this project. Considering the order in which these activities need to occur, she also has constructed the following project network.

Using the PERT three-estimate approach, Sharon has obtained the following estimates of the duration of each activity.

(a) Find the estimate of the mean and variance of the duration of each activity.

(b) Find the mean critical path.

(c) Use the mean critical path to find the approximate probability that the advertising campaign will be ready to launch within 57 days.

(d) Now consider the other path through the project network. Find the approximate probability that this path will be completed within 57 days.

(e) Since these paths do not overlap, a better estimate of the probability that the project will finish within 57 days can be obtained as follows. The project will finish within 57 days if both paths are completed within 57 days. Therefore, the approximate probability that the project will finish within 57 days is the product of the probabilities found in parts (c) and (d). Perform this calculation. What does this answer say about the accuracy of the standard procedure used in part (c)?

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