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Moore Housing Contractors is negotiating a deal with Countryside Realtors to build six houses in a new development. Countryside wants Moore Contractors to start in late winter or early spring when the weather begins to moderate and build through the summer into the fall. The summer months are busy for the realty company, and it believes it can sell the houses almost as soon as they are ready-sometimes before. The houses all have similar floor plans and are of approximately equal size; only the exteriors are noticeably different. The completion time is so critical for Countryside realtors that it is insisting a project management network accompany the contractor's bid for the job with an estimate of the completion time for a house. The realtor also needs to be able to plan its offerings and marketing for the summer. The realtor wants each house to be completed within 42 days after it is started. If a house is not completed within this time frame, the realtor wants to be able to charge the contractor a penalty. The MHC is concerned about the prospect of a penalty. They want to be confident they can meet the house's deadline before entering into any agreement with a penalty involved. Moore has experienced house builders, so it was not difficult for them to list the activities involved in building a house or estimate activity times. However, they made their estimates conservatively and tended to increase their pessimistic estimates to compensate for the possibility of bad weather and variations in their workforce. Table 1 shows a list of the activities for building a house and the activity time estimate. 1. Develop a network diagram for MHC and determine the probability that the contractors can complete a house in 42 days or less. DO NOT round up/down the calculated expected time. Keep it at two decimal points. Table 1 Activity a b e f C g i J k 1 Description Excavation, pour footers Lay foundation Frame and roof Sewer (floor) drains Install insulation Pour basement floor Install windows Rough electrical wiring Install furnace Exterior brickwork Install plasterboard Roof shingles Attach gutter Grading Lay subflooring Lay driveway Kitchen, sink, appliances Painting Finish wood floor Time (Days) Predecessor none 3 a 2 b 2 b 1 2 e 2 f 1 f 1 C,8 3 i 5 jik 6 1 2 n 1 2 m 3 4 2 t 4 2 m 4 3 4 2 4 3 3 2. 5 6 8 3 2 3 4 6 4 6 5 b 6 5 5 3 5 5 4 4 8 10 12 6 5 7 6 10 8 10 8 ESO q 3