$1.$ A project involves eight activities as depicted in the figure below duration in days$).$ Assume that the client has requested to complete the project in $40$ days.

Answer the following questions:

$(1)$ Identify the critical path for the project, and determine the earliest and latest times that the project can be completed.

$(2)$ Assume that Activity A actually finished on Day $8,$ what is the total slack for Activity B now? If you were the project manager, what are the actions you would recommend in order to get the project back on schedule? Justify your answers.