Semiautomatic mixers are used to mix a particular chemical. It requires 5 minutes to load a mixer; the mixer runs automatically and produces a batch of 1000 gallons of chemical before automatically unloading. The automatic mixing time equals 60 minutes. The automatic unloading time equals 4 minutes. Travel between machines requires 15 seconds. While mixers are automatically mixing chemicals the operator performs a quality control inspection on the previous bath, which requires 5 minutes per batch. An operator costs $15 per hour; each mixer costs $80 per hour.
(a) Determine the number of mixers to be assigned per operator to minimize the cost per batch produced.
(b) Suppose that there are 15 mixers to be assigned. How should they be assigned to minimize the long-run cost per batch?
(c) For what range of inspection time will the optimum number of mixers per operator be 7?