Seven parts P1 to P7 are machined first on a milling machine and then polished at a separate machine. Using the processing times (in hours) given below, find the minimum total elapsed time required to complete both operations for all 7 parts. - P1: Milling = 8, Polishing = 6 - P2: Milling = 3, Polishing = 2 - P3: Milling = 3, Polishing = 4 - P4: Milling = 4, Polishing = 6 - P5: Milling = 5, Polishing = 7 - P6: Milling = 6, Polishing = 4 - P7: Milling = 2, Polishing = 1

A PERT network has 9 independent activities on its critical path. If the standard deviation of each activity on the critical path is 3, what is the standard deviation of the critical path?

Which of the following statements correctly describe detection conditions for special cases in the Simplex Method? I. Unboundedness is indicated when all elements in a pivot column are ≤ 0. II. Degeneracy occurs when a tie in the minimum ratio test produces a basic variable with zero value. III. Alternate optimal solutions exist if a basic variable has Cj - Zj = 0 in the optimal tableau. IV. Infeasibility is indicated if an artificial variable remains in the optimal basis at a positive level. Choose the correct option: