Semiautomatic mixers are used in a paint plant. It takes 5 minutes for an operation to load the appropriate pigments and paint base into a mixer. Mixers run automatically and then automatically dispense paint into 75-gallon drums, which takes 25 minutes to complete. Operators clean the mixers between batches which takes 2 minutes. Between batches, an operator prepares empty drums to position them for filling which takes 3 minutes. Filled drums are transported automatically by a conveyor to a test area before being stored.
Mixers are located close enough for travel between mixers to be negligible.

a. What is the maximum number of mixers that can be assigned to an operator without creating idle time for the mixers?

b. If the operator cost is $17/hour and the machine cost is $28/hour, what assignment of mixers to operators will minimize the cost per batch produced?