Your company has just received an order for a specially designed electric motor. The contract states that if the project is not completed 12 days from now, then beginning on the 13th day, your firm will experience a penalty of $300 per day. The table below shows the activities that need to be completed for this project, along with data on direct costs and precedence relations. (Crash Time represents the minimum activity time if it was completely crashed; the Crash Cost represents the cost of each activity if it is crashed to its minimum.)

a) Draw the network diagram (only draw Activity on Node).

b) Find the critical path(s). What is the normal duration (i.e. without crashing) of the entire project?

c) What is the slack time of activity D?

d) Right now, would you rather incur the late cost of $300 per day, or would you want to crash the project at some cost? What is the project completion time that you recommend for this project? Remember: it will be better to incur the penalty cost if the cost of reducing the project duration is greater than $300 per day. What are the activities that you crash, and by how much? What is the total project cost for your recommended project length?

\begin{tabular}{cccccc} \hline Activity & \begin{tabular}{c} Normal \\ Time (days) \end{tabular} & \begin{tabular}{c} Normal \\ Cost ($) \end{tabular} & \begin{tabular}{c} Crash Time \\ (days) \end{tabular} & \begin{tabular}{c} Crash Cost \\ ($) \end{tabular} & \begin{tabular}{c} Immediate \\ Predecessors \end{tabular} \\ \hline A & 4 & 1000 & 3 & 1300 & None \\ B & 7 & 1400 & 4 & 2000 & None \\ C & 5 & 2000 & 4 & 2700 & None \\ D & 6 & 1200 & 5 & 1400 & A \\ E & 3 & 900 & 2 & 1100 & B \\ F & 11 & 2500 & 6 & 3750 & C \\ G & 4 & 800 & 3 & 1450 & D, E \\ H & 3 & 300 & 1 & 500 & F, G \\ \hline \end{tabular}