R. C. Coleman distributes a variety of food products that are sold through grocery store and supermarket outlets. The company receives orders directly from the individual outlets, with a typical order requesting the delivery of several cases of anywhere from 20 to 50 different products. Under the company's current warehouse operation, warehouse clerks dispatch order- picking personnel to fill each order and have the goods moved to the warehouse shipping area. Because of the high labor costs and relatively low productivity of hand order picking, management has decided to automate the warehouse operation by installing a computer- controlled order-picking system, along with a conveyor system for moving goods from storage to the warehouse shipping area. R. C. Coleman' director of material management has been named the project manager in charge of the automated warehouse system. After consulting with members of the engineering staff and warehouse management personnel, the director compiled a list of activities associated with the project. The optimistic, most probable, and pessimistic times (in weeks) have also been provided for each activity. They have also estimated that the project will be ready to start on March 1st. Most ABCDE Activity Description Determine equipment needs Obtain vendor proposals Predecessor Optimistic Probable Pessimistic 4 6 8 Select vendor A, B Order system C Design new warehouse layout C 628N 8 4 10 7 10 F Design warehouse E 4 6 G Design computer interface C 4 6 H Interface computer D, F, G 4 6 I Install system D, F 4 6 J Train system operators H 3 4 K Test system I, J 2 4 6623828150 24 14 1. Calculate the expected value and variance of the times for all the activities. 2. Do and AON diagram to find the critical path using the expected times. Identify the critical activities and find the slack time for the others. 3. Do a Gantt Chart to visualize better the project scheduling (submit the graph in Canvas). 4. Develop a report that presents the activity schedule and expected project completion time for the warehouse expansion project. 5. When is the project expected to be finished? 6. When would be the earliest that the system operators training can start? 7. R. C. Coleman's top management established a required 40-week completion time for the project. Can this completion time be achieved? Include probability information in your discussion. What recommendations do you have if the 40-week completion time is required? 8. What is the probability that the warehouse design is finished by September 6th?