A product arrives according to a Poisson distribution at the rate of one every 45 minutes.

The product requires two tandem operations attended by one worker. The first operation uses a semiautomatic machine that completes its cycle in exactly 28 minutes.

The second operation makes adjustments and minor changes, and its time depends on the condition of the product when it leaves operation 1. Specifically, the time of operation 2 is uniform between 3 and 6 minutes. Because each operation requires the complete attention of the worker, a new item cannot be loaded on the semiautomatic machine until the current item has cleared operation 2.

(a) Determine the number of items awaiting processing on the semiautomatic machine.

(b) What is the percentage of time the worker will be idle?

(c) How much time is needed, on the average, for an arriving item to clear operation 2?