Question

Consider a 5-step process for the National Corporation that includes cutting, drilling, stamping, welding, and painting. The cutting department has 6 machines that each process materials at a rate of 2 minutes per unit. Drilling has 6 machines that each process materials at a rate of 3 minutes per unit. Stamping has 6 machines that each process materials at a rate of 4 minutes per unit. Welding has 4 machines that each process materials at a rate of 2 minutes per unit. Painting has 2 machines that each process materials at a rate of 4 minutes per unit. What is the capacity of the entire five-step process in units per hour? Please enter your answer rounding down to the nearest completed unit.

Answer 1

`\large\boxed{\large\boxed{\text{The capacity of the entire five-step process is 30 units per hour}}}`

Step-by-step explanation:

The rate of production is determined by the slowest step or process.

Determine the rate of production of each step.

1. The Cutting department has 6 machines that each process materials at a rate of 2 minutes per unit.

• rate = number of machines × rate of each machince

• rate = 6 × 1 unit / 2 minute = 3 units / minute

2. Drilling has 6 machines that each process materials at a rate of 3 minutes per unit.

• rate = number of machines × rate of each machince

• rate = 6 × 1 unit / 3 minute = 2 units / minute

3. Stamping has 6 machines that each process materials at a rate of 4 minutes per unit.

• rate = number of machines × rate of each machince

• rate = 6 × 1 unit / 4 minute = 1.5 units / minute

4. Welding has 4 machines that each process materials at a rate of 2 minutes per unit.

• rate = number of machines × rate of each machince

• rate = 4 × 1 unit / 2 minute = 2 units / minute

5. Painting has 2 machines that each process materials at a rate of 4 minutes per unit.

• rate = number of machines × rate of each machince

• rate = 2 × 1 unit / 4 minute = 0.5 units / minute

Then, the fifth process, painting is the slowest process because it only can process 0.5 units per minute. This is the bottleneck. Even if the other processes worked faster, the production could not exceed the number of machines that can be painted per hour.

To find how many units can be painted or produced by hour multiply the rate by the number of minutes in one hour:

• 0.5 units/min × 60 min/hour = 30 units / hour.

Therefore, the capacity of the entire five-step process is 30 units per hour.