1)__(18 pts) Many complex projects can be described as a series of stages where each stage represents a sub-project (e.g., the design, coding, and testing of a new IT product). This is especially true for new product development (NPD) projects, where a “stage-gate” or “toll-gate” can be used between stages to monitor the development process. In this problem, we consider a NPD project that consists of three stages: Stage Start Stage Stage End The duration of each stage is a random variable that is described by a discrete probability distribution as given below. Stage B Stage C Duration Probability | Duration Probability 20 0.3 0.7 0.9 12 Stage A Duration Probability 0.6 0.2 0.2 E[makespan] 13.6 0.1 E[makespan] 23.5 E[makespan 8 .8 a) What is the expected makespan of this project? What is the probability that the project will require at least 47 days? (Do NOT use Monte-Carlo simulation in this problem.) b) Stage A was just completed in 18 days. Using this information, what is your updated estimate of the expected project makespan? What is your updated probability that the project will need at least 47 days?