The team realizes that the project will take longer than they thought and informs senior management. Having expected a much shorter delay to implement this change, they would like you to propose ways to shorten the delay. There are indeed a few ways that you could reduce the duration of some activities. For example, the installation crew could work overtime for some activities, or you could find a more expensive supplier with a shorter delivery delay. You have therefore compiled the following table with the maximum reduction (in days) for each activity and the associated costs. Each activity may be reduced by one day at a time. However, some activities may be reduced by more than one week. For example, if we want to reduce activity E by 2 days, it will cost 2*100$ = 200$. Considering the reduction limits and acceleration costs presented in the table below, determine the shortest possible project duration, as well as the investment required. Justify your answer.

NOTE: For each iteration, indicate the critical path(s), the activity or activities to accelerate, the number of weeks accelerated and the acceleration cost

\begin{tabular}{|c|c|c|} \hline Activity & Maximumreduction(days) & Accelerationcost(S/day) \\ \hline A & & \\ \hline B & 6 & 75 \\ \hline C & 5 & 100 \\ \hline D & 4 & 250 \\ \hline E & 3 & 100 \\ \hline F & & \\ \hline G & & \\ \hline H & & \\ \hline I & 2 & 550 \\ \hline J & & \\ \hline K & 2 & 500 \\ \hline L & 4 & 850 \\ \hline M & & \\ \hline \end{tabular}