Final answer:
The specific batch size for countertop A requires additional information about the production cycle or schedule. The batch size would ensure demand is met and inventory minimized, considering the production rate and setup times.
Step-by-step explanation:
The question asks us to determine the batch size for countertop type A given the production cycle ISEN (A B C D A B C D...) and the demand rates for each countertop type (A: 100 feet/hr, B: 80 feet/hr, C: 70 feet/hr, and D: 50 feet/hr), with a production rate of 350 feet/hr.
To calculate the batch size for countertop A, we first need to determine the total production time spent on each countertop to satisfy one hour of demand. Since the demand rate for A is 100 feet/hr and the production cell can produce 350 feet/hr, we can cover the demand for A in (100 feet/hr) / (350 feet/hr) = 0.2857 hours, or approximately 17.14 minutes.
However, because there is a 3-hour setup time required whenever switching types, the batch size selected should be large enough to minimize these switches and thus reduce downtime. Assuming all types require the same setup time and that they will be produced in equal proportions over time to meet demand, we can determine the batch size for A by:
- Multiplying the demand rate for A by the total cycle time (including setup times)
- Adding the setup times for each type (3 hours for each)
- Dividing by the production rate of 350 feet/hr to get the batch size
Unfortunately, without additional information on the number of cycles or a more detailed production schedule, we cannot calculate the specific batch size for countertop A. We would need this information to account for the demand of each countertop type within the cycle and to allocate the proper amount of production time to each to minimize inventory and satisfy demand.