1. Consider a two-station production line in which no inventory is allowed between stations (i.e. the stations are tightly coupled). Station 1 consists of a single machine that has potential daily production of one, two, three, four, five, or six units, each outcome being equally likely (i.e., potential production is determined by the roll of a single die). Station 2 consists of a single machine that has potential daily production of either three or four units, both of which are equally likely (i.e., it produces three units if a fair coin comes up heads and four units if it comes up tails). (a) Compute the capacity of each station (i.e., in units per day). Is the line balanced (i.e., do both stations have the same capacity)? (b) Compute the expected daily throughput of the line. Why does this differ from your answer to (a)? (c) Suppose a second identical machine is added to station 1. How much does this increase average throughput? What implications might this result have concerning the desirability of a balanced line? (d) Suppose a second identical machine is added to station 2 (but not station 1). How much does this increase average throughput? Is the impact the same from adding a machine at stations 1 and 2? Explain why or why not.