2.10. Parts arrive at a painting machine according to a Poisson process with rate X/h. The machine can paint one part at a time. The painting process appears to be exponential with an average service time of 1/ h. It costs the company about $C per part per hour spent in the system (i.e., being painted or waiting to be painted). The cost of owning and operating the painting machine is strictly a function of its speed. In particular, a machine that works at an average rate of u costs $uC2/h, whether or not it is always in operation. Determine the value of u that minimizes the cost of the painting operation.