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: 7 weeks
assume the minimum cycle length $t = 6$ weeks is used
minimum batch size for one flavor:
$6 \text{ wks} \times 4,800 \text{ pints/wk} = 28,800 \text{ pints}$
average inventory for one flavor:

Explanation:

Step1: Define key variables

Let $D = 4800$ pints/week (demand per flavor), $T = 6$ weeks (cycle length), $P = 28800$ pints/week (production rate)

Step2: Find production time per flavor

First, calculate total production needed per cycle: $Q = D \times T = 4800 \times 6 = 28800$ pints.
Production time $t_p = \frac{Q}{P} = \frac{28800}{28800} = 1$ week

Step3: Calculate max inventory per flavor

Inventory builds at rate $P-D$, so max inventory $I_{max} = (P-D) \times t_p$
$I_{max} = (28800 - 4800) \times 1 = 24000$ pints

Step4: Compute average inventory

Average inventory is half of max inventory: $\frac{I_{max}}{2}$
$\frac{24000}{2} = 12000$ pints

Answer:

12000 pints