PART III. EXTENDED PROBLEMS Problem 1 (20points) This question focuses on a factory that manufactures plastic dolls. Each doll is made up of a head, two arms, two legs, and a torso. The factory would like to produce 95 dolls in each 8 hour working day. The process for producing a doll can be summarized as follows: Task Task Time Predecessors (Minutes) 5 3 2 1 1 1 2 1. Mold head, arms, legs, and torso 2. Trim excess plastic from arms and legs 3. Trim excess plastic from head 4. Trim excess plastic from torso 5. Print Box 6. Paint face on head 7. Sew hair to head 8. Snap legs, arms, head, and torso together 9. Package 3 3 3 5 6 2 2, 4, 7 5,8 5 1. (5 points) Draw the precedence diagram for the tasks at the doll manufacturer. 2. (3 points) Determine the desired cycle time. 3. (2 point) Determine the theoretical minimum number of stations needed. 4. (4 points) Assign tasks to stations in a forward manner using most following tasks priority rule. Write clearly in which order tasks are selected by the priority rule and which tasks are assigned to which station