2.10. Parts arrive at a painting machine according to a Poisson process with rate X/h. The...

 

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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/μ h. It costs the company about $C₁ 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. 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/μ h. It costs the company about $C₁ 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.

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Clearly the operation of this station can wik be modeled as an MMI queue azzival rate ... View the full answer