$11\mathrm{.}9$Planmatics is undertaking a modernization program. The set of activities in Table $11\mathrm{.}16$ has been defined for refurbishing one of its wave soldering machines. The AOA network is given in Figure $11\mathrm{.}5.$ a$.$Find the critical path, total slacks, and free slacks. b$.$Find the probability of completion within $45$ days. c$.$Find the minimum cost increase to reduce the expected project duration by $1$ day. d$.$Find the minimum cost increase to reduce the expected project duration by $2$ days. e$.$Find the minimum project duration and the expected cost increase.