A donut store is open 8 hours a day and sells two types of donuts – blueberry cake donut and chocolate frosted donut. On average the demand is 80 donuts per day for EACH type. The store has only one machine which makes both types, and once it starts, it produces one donut every 2 minutes for either type. The production alternates between the two types, i. e., a batch of one type is followed by a batch of the other. The setup time is 20 minutes for either type. Assume the same batch size all the time for both types.

(a) If the batch size is 10 donuts per batch, what is the capacity per day for each type of donut?
(b) What is the minimal batch size in order to satisfy demand for both types?

Part A)

Processing time for Each Batch = Setup time + Production time

Processing time for Each Batch = 20 + 2 × 10

Processing time for Each Batch = 40 minutes

Thus,

Capacity for one day = Total working Hour / processing time

Capacity for one day = 8 hours / 40 minutes

Capacity for one day = 12 batches

(6 batches of each donuts type, or 60 donuts of each type)

Part B)

Total production time for both donuts = (80 + 80) × 2

Total production time for both donuts = 320 minutes

Time for Total batch = 480 - 320

Time for Total batch = 160 minutes

Batch time available for each type = 160 / 2

Batch time available for each type = 80 minutes.

Number of batches = 80 minutes / 20 minutes

Number of batches = 4 batches

Thus,

Minimal batch size = 80 donuts / 4 batches

Minimal batch size = 20 donuts for each type of donuts in single batch.

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