In the following AON project network, the estimated normal durations for each task are indicated at each node. Each task in this project can be compressed by a maximum of two weeks; each week's decrease will cost an amount that is equal to its estimated normal duration $($for example, the duration of task A can be reduced to six weeks by spending an additional $$7K,$ or it can be reduced to five weeks for an additional cost of $$14K).$

a$.$ w nicn tasks snouid de compressed in we want to reauce tne project by tnree weeks at the smallest possible total dost? What is the marginal increase in total cost for each week that we decrease the project duration?

b$.$ If the project is completed after twenty weeks, a penalty fee of $$9K$ per week is assessed for each late. However, if the project is completed before $20$ weeks, there is a bonus paid of $$5K$ for each early. Find the project duration that minimizes the total cost.