Question

multi-product process with setups
demand: 4,800 pints/week for each of 5 flavors
production rate: 6 pints/minute = 28,800 pints/week
setup time: 0.2 weeks, regardless of flavor
cycle 1, length: t weeks
assume the minimum cycle length $t = 6$ weeks is used
minimum batch size for one flavor:

Explanation:

Step1: Calculate total setup time

Total setup time = Number of flavors × Setup time per flavor
Total setup time = $5 \times 0.2 = 1$ week

Step2: Calculate available production time

Available production time = Cycle length - Total setup time
Available production time = $6 - 1 = 5$ weeks

Step3: Calculate total production needed

Total weekly demand = $5 \times 4800 = 24000$ pints/week
Total demand in cycle = $24000 \times 6 = 144000$ pints

Step4: Verify production capacity matches demand

Total production capacity in available time = $28800 \times 5 = 144000$ pints (matches total demand)

Step5: Calculate batch size per flavor

Batch size per flavor = Demand per flavor × Cycle length
Batch size per flavor = $4800 \times 6 = 28800$ pints

Answer:

28800 pints