Bonda Motors runs a large service facility. In the facility, when needing parts to fix automobiles, mechanics have to fill out the parts request form and wait at the parts counter before being handed over the part requested. Mechanics arrive at the counter based on Poisson arrival process at a rate of 30 per hour. The service time at the parts counter is exponentially distributed with a mean of 10 per hour. The mechanic's average wage is $75 per hour and the average wage for a part's clerk is $30 per hour. Both the mechanics and the part counter clerks put in 8 hours of labor every day. Assume population source to be infinite, rationalized partly on rather high arrival rate of the mechanics.
How many parts counters would you recommend if the objective is to minimize the total cost while maintaining proper service?