Question: Three independent widget-producing machines all require the same type of vital part, which needs frequent maintenance. To increase production it is decided to keep two spare parts on hand (for a total of 2 + 3 = 5 parts). After 2 hours of use, the part is removed from the machine and taken to a single technician, who can do the required maintenance in 30 ± 20 minutes. After maintenance, the part is placed in the pool of spare parts, to be put into the first machine that requires it The technician has other duties, namely, repairing other items which have a higher priority and which anive every 60 ± 20 · minutes requiring 15 ± 15 minutes to repair. Also, the technician takes a 15-minute break in each 2-hour time period. That is, the technician works 1 hour 45 minutes; takes off 15 minutes, works 1 hour 45 minutes, takes off 15 minutes, and so on.

(a) What are the model's initial conditions-that is, where are the parts at time O.and what is their condition? Are these conditions typical of "steady state"?

(b) Make each replication of this experiment consist of an 8-hour initialization phase followed by a 40-hour data-collection phase. Make four statistically independent replications of -the experiment all in one computer ron (i.e.; make four rons with each using a different set of random nurnbers);

(c) Estimate the mean number of busy machines and the proportion of time the technician is busy.

(d) Parts are estimated to cost the company $50 per part per 8-hour day (regardless of how much they are in use). The cost of the technician is $20 per hour. A working machine produces widgets worth $100 for each hour of production. Develop an expression to represent total cost per hour which can be attributed to widget production (i.e., not all of the technician's time is due to widget production). Evatuate this expression, given the results of the simulation.