Problem 5.50 An inventory control model. Consider a warehouse containing an inventory of 10 high voltage transformers. If at the end of the week the inventory level falls below 2 (≤ 2), an order is placed to return the inventory level to 10. Suppose orders per week arrive according to a Poisson process with λ = 6.

(a) Find the probability that at the end of the week the inventory falls below 2.

(b) Find the probability that at the end of the week the demand for the transformers exceeds the initial inventory, i.e., the number of transformers ordered is ≥ 11.