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Consider a project network with four activities, their normal durations, their shortest possible durations (which can be achieved at extra cost), \& the acceleration cost per time unit. (a) Draw the project network. (b) Use the forward recursion, the backward recursion, calculate the floats, \& determine the critical path(s). What is the duration of the project? (c) Accelerate the project by one day. Clearly indicate which (combinations of) activities could be accelerated in order to speed up the project, \& which activity or activities should be accelerated. What are the associated costs? (d) Back to the network with the original (normal) durations. Suppose the resource consumptions of the four activities are 110,190,220,&130, respectively. Schedule all activities as carly as possible \& draw the appropriate Gantt chart. What is the highest resource requirement at any point in time? If we had to hire employees for the duration of the entire duration of the project, what is the proportion of time that employees will be idle