Question

C&A makes two types of products using four machines from 9 a.m. to 5 p.m. each day. Product A visits machines 1, 2, and 4. Product B only visits machines 1 and 3. The capacity is 0.4 unit per minute at machine 1, 0.12 unit per minute at machine 2, 0.2 unit per minute at machine 3, and 0.3 unit per minute at machine 4. The demand per day is 40 units for Product A and 160 units for Product B.

A. What is the implied utilization rate for each of the machine?

B. Where is the bottleneck?

C. What is the flow rate for Products A and B?

Answer 1

The utilization rate for each machine is the demand divided by the capacity multiplied by the total available time. The machine with the highest utilization rate is the bottleneck, which limits the maximum flow rate of production for both products.

Step-by-step explanation:

The student is asking about the utilization rates of machines, identifying the bottleneck in production, and determining the flow rate for two products. To find the utilization rate, divide the demand by the capacity of each machine and then multiply by the total available time. The bottleneck is the machine with the highest utilization rate, impeding the flow rate of products. The flow rate is the capacity of the bottleneck machine because it limits the maximum production rate of both products.

Given that the demand for Product A is 40 units and for Product B is 160 units per day, we can calculate the total minutes available for production as 8 hours (from 9 a.m. to 5 p.m.), times 60 minutes, which equals 480 minutes per day.

Machine capacities per day are: Machine 1 - 192 units, Machine 2 - 57.6 units, Machine 3 - 96 units, and Machine 4 - 144 units. The utilization rate is the demand for each product divided by the capacity of the necessary machines. The bottleneck is the machine with the highest utilization rate, which limits overall production.