$17.$ For the network shown: a$.$ Determine the critical path and the early completion time in weeks for the project b$.$ For the data shown, reduce the project completion time by three weeks. Assume a linear cost per week shortened, and show, step by step, how you arrived at your schedule. Activity Normal Time Normal Cost Crash Time Crash Cost A $5$ $$7,0003$ $$13,000$ B $10$ $$12,0007$ $$18,000$ C $8$ $$5,0007$ $$7,000$ D $6$ $$4,0006$ $$5,000$ E $7$ $$3,0006$ $$6,000$ F $4$ $$6,0003$ $$7,000$ G $4$ $$7,0003$ $$9,000$ PLEASE SHOW ALL WORKING AND HOW THE SOLUTION WAS OBTAINEDThe following table represents a plan for a project:

a$.$ Construct the appropriate network diagram.

b$.$ Indicate the critical path.

c$.$ What is the expected completion time for the project?

d$.$ You can accomplish any one of the following at an additional cost of $$1,500$ :

$(1)$ Reduce job $5$ by two days.

$(2)$ Reduce job $3$ by two days.

$(3)$ Reduce job $7$ by two days.

If you will save $$1,000$ for each day that the earliest completion time is

reduced, which action, if any, would you choose?

e$.$ What is the probability that the project will take less than $30$ days to complete?