Alex is solving a transportation problem for his project. Assuming that he is not allowed to use any computer support, he has three algorithms to apply for finding a basic feasible solution (BFS): North-West Corner method (Method 1), Minimum Cost method (Method 2), and Vogels method (Method 3). It is known that Minimum Cost method and Vogels method are not providing a feasible solution for this specific problem. The amount of minutes necessary to apply Method 1 is a uniform random variable defined over (4, 10). The amount of minutes needed to apply Method 2 is a normally distributed random variable with = 9 and = 3. The amount of minutes necessary for finding a BFS with Method 3 is exactly 6 minutes (not random). Assuming that Ahmet is equally likely to select one of the three methods,

a) What is the expected amount of minutes that it takes him to find a BFS (assuming that he has a memory)?

b) Suppose that Ahmet has no memory, what is the expected amount of minutes that it takes to him to find a BFS?