$4.$ A company is planning a small project for a particular client and the following table gives the various activities in that project, as well as their associated completion times. Here, for example, activity D takes $6$ days to be completed. The immediate precedence relationships are: In addition, three other conditions $($X$1,$ X$2$ and X$3)$ must apply: Condition X$1$: $9$ days must elapse between the end of activity B and the start of activity E $*$ Condition X$2$: $1$ day must elapse between the end of activity B and the start of activity C $*$ Condition X$3$: $7$ days must elapse between the end of activity C and the start of activity $\backslash ($ F $\backslash )($a$)$ Draw the network diagram and calculate the overall project completion time. State the critical paths. $($b$)$ Copy the following table into your answer book and fill in the latest start times. $(6$ marks$)($c$)$ The company is aiming to finish the project as soon as possible. However, it has given a clear commitment to their client that the latest time by which activity D will start is $14$ days after the start of the project. In the light of this and your calculations above what should the company do$?(4$ marks$)($d$)$ Explain what is meant by the term 'resource smoothing' in relation to project management. $(6$ marks$)$