Consider a 3-stage production process where units must pass through all stages, and stage 1 must be completed before stage 2 can start and stage 1 cannot produce to work-in- process inventory etc. Each stage will have the potential to produce either two, three four, five or six units of output each hour with equal probability (1/5). The stages are stochastically independent. Stage 1 has a constant and unlimited supply of raw materials.

a)What is the expected (or average) output of this 3-stage production process?

b)What is the average time stage 1 is idle while waiting for stage 2?

c)How many units are on average lost to wait-time every hour?

d)Suppose investing in process improvement at either of the 3 stages eliminates the chance that only 2 units is produced but retains an even chance of potential output levels three, four, five or 6. Which of the 3 stages would you improve on first? Discuss why and provide supporting calculations.