Salem Daughters Construction Company has contracted with a Mr. Hawthorne to build a classic house having seven gables. The customer wants to complete the house as soon as possible, at a minimum cost. The preliminary data in Table 19-14 apply for the various activities. Table 10-14 Data for the Construction Activities 10000 Jas the Excavate (c) (d) (e) C (8) Activity Floor joists Exterior plumbing (6) Floor (M) Power on (2) Walls () Wire (A) Comline (1) (n) (0) (0) (0) in (5) (0) Basement Foundation Inside plumbing dows Doors Sheetrock Interior trim Exterior trim Paint Carpet Buyer inspection Activity Cost $1.000 2.500 4,400 5.500 2,000 Temecatays Preceding Activity Activity Cost $ 500 3,000 & h a.c d Samantha Salem believes that the data in Table 19-14 reflect optimal expen- ditures of labor and resources. The following cost estimates correspond. 500 4,000 2.300 A.C 0,1 no m. p. g. Ex Completion T Activity Cost $200 1,500 2,300 1.000 3,200 7 m n 0 Activity Cost $8,000 3,000 3,000 5,000 0 d F Q The preceding includes the cost of materials supplied by subcontractors. Ad- ditional Salem materials costs are $51,000. A few activities can be speeded up. By working extended hours, carpenters can complete the walls in 8 days at a total cost of $4,500. Working at night,work- ers can complete the sheetrock in 2 days at a total cost of $3,500. For a premium of $700, the plumbing contractor can complete inside plumbing in 3 days. Using night lighting, crews can finish the excavation in 2 days at a total cost of $3,500 and complete the grading in 2 days for $1,600. SE 1. Construct a PERT network for the project, entering the expected activity completion times alongside the applicable arrows. 2. For each event, find the earliest possible, latest allowable, and slack times. Then, establish the critical path. How long is the project expected to take? 3. Determine a sequence of plans for Salem Daughters Construction Company, each plan representing a 1-day savings in project completion time at a mini- mal increase in cost. 4. Salem has accepted an incentive clause which provides for a payment of $400 for each day saved from an anticipated 40-day duration until project completion. Which plan identified in Question 3 should be implemented? Specify which activities should be speeded up and by how many days. What is Salem's net project cost using the optimal plan? 5. Analysis in Questions 1-4 has all been based on expected activity comple- tion times. Samantha is concerned that the uncertainties in the project have so far been downplayed. The expected activity completion times given ear- lier were computed from the three time estimate data (in days) given in Table 19-15. Compute the variance in completion time for each activity. 6. The modified beta distribution for each activity time (1) is positively skewed if m is closer to a than to b, (2) is symmetrical if m falls midway between a and b. (3) is negatively skewed if m is closer to & than to a, and (4) has zero variance if a, m, and bare all equal. (a) Determine for each activity which case applies. (b) For the zero-variance activity times, what may you conclude regarding the completion time probabilities? 7. Consider the critical path found in Question 2. (a) Find the variance for the duration of that path. (b) Determine the probability that the path will take more than 42 days. Tubio US Three Time Estimate Data for the Construction Activities Activity Orade (Excavate (c) Basement (0) Foundation fet Floor joists (f) Exterior plumbing Floor Power on Walls (Wire (K) Com lines Un Inside plumbing um Windows Doors to) Shoetrock (p) Interior trim. (0) Extenor trim (Paint (5) Carpet (t) Buyer inspection Optimistic Most Likely Time Time 5.25 3 4.75 4 1 Pessimistic Time 8. Consider the "nearly" critical path b-cd-e-gi-j-k-op-rs-t (a) Find the expected duration and variance of that path. 10 NANNA 55 (b) Determine the probability that the path will take more than 42 days. (c) Compare your answers in Question 7(b). What may you conclude re- garding using any single-path probability to estimate a probability for project completion time?