Semi-automatic mixers are used to mix a particular chemical. It takes 5 minutes to charge a mixer; The mixer works automatically and produces a 1000-gallon batch of chemicals before automatically discharging it. The automatic mixing time is 60 minutes. The automatic download time is 4 minutes. The journey between machines requires 15 seconds. While the mixers automatically mix the 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 that will be assigned per operator to minimize the cost per batch produced.

(b) Suppose there are 15 mixers to be allocated. How should they be allocated to minimize the long-run cost per lot?

(c) For what range of inspection time will the optimal number of mixers per operator be 7?