A project has the following duration of activities. The arcs are representing the activities and durations are representing the time

in days to complete that activity.

a$.$ As a Project Manager you need to find the longest duration that this project will take to complete all the activities keeping in

view the precedence relationship of activities. Formulate a Linear Program for this problem and write down its dual explaining

all the variables and constraints.

b$.$ Solve the above problem using Complementary Slackness Theorem by clearly showing the steps.