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In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are three machine tools, four polishing tools, and three painting tools, how many different routings (consisting of machining, followed by polishing, and followed by painting) for a part are possible?

Short Answer

Expert verified
There are 36 different routings possible for producing the part.

Step by step solution

01

Identify the Processes

The process of producing a part involves three stages: machining, polishing, and painting.
02

Determine the Number of Options per Process

There are 3 machine tools for machining, 4 polishing tools for polishing, and 3 painting tools for painting.
03

Calculate Possible Options for Machining

There are 3 choices for the machining process since there are 3 machine tools available.
04

Calculate Possible Options for Polishing

There are 4 choices for the polishing process since there are 4 polishing tools available.
05

Calculate Possible Options for Painting

There are 3 choices for the painting process since there are 3 painting tools available.
06

Calculate Total Number of Routings

The total number of different routings is the product of the number of choices for each process: \(3 \times 4 \times 3\).
07

Perform the Calculation

Multiply the choices: \(3 \times 4 = 12\) and then \(12 \times 3 = 36\).
08

Conclusion

There are a total of 36 different routings possible for producing the part.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Machining Process
In the manufacturing world, the machining process is often the first crucial step in transforming a raw material into a finished product. This process involves the use of machine tools to critically shape and dimension the material. Using tools like lathes, milling machines, or drill presses, materials are cut, drilled, or shaped to precise specifications. 
Choosing the right machine tool is vital as it affects the quality and speed of production. In scenarios where there are multiple machines, like in our exercise with three available machines, operators must decide which machine to use based on factors like the type of material, precision level required, and the complexity of shapes that need to be produced.
  • Precision: The level of accuracy needed influences which machine is suitable for the job.
  • Material Type: Different machinery might be needed for metals versus plastics.
  • Complex Shapes: Advanced machines can handle intricate designs better.
The choice of the machine not only impacts the efficiency but also the cost-effectiveness of the production process.
Polishing Techniques
Following machining, polishing comes into play to enhance the surface finish of the produced part. Polishing involves using tools with abrasives to smooth out any surface irregularities, scratches, or marks introduced during machining. This step is key in ensuring that the product meets the desired aesthetic and functional quality.
There are several polishing techniques available, and the suitability of each technique depends on the material and desired finish. In our scenario, having four polishing tools means one can select tools based on specific needs and results intended.
  • Mechanical Polishing: Involves the use of abrasives and machinery for high-efficiency polishing.
  • Electrochemical Polishing: Uses electrical current to remove material, perfect for metals.
  • Manual Polishing: Often used for delicate or sensitive parts requiring a soft touch.
Each technique can achieve varying degrees of reflection and smoothness, impacting the part's final application.
Painting Methods
The painting process is the final touch to a manufactured product, providing both protection and aesthetics. It involves applying a coat of paint to the surface, which can add color, prevent corrosion, and ensure the part looks visually appealing. The exercise notes three painting tools to choose from, each offering different methods and results.
Choosing an appropriate painting method is influenced by factors like the material of the part, the environment it will be exposed to, and the finish quality desired.
  • Spray Painting: Offers smooth and even coatings, suitable for large surfaces.
  • Powder Coating: Durable and suitable for metals, it's applied electrostatically and then cured under heat.
  • Brushing: A cost-effective way to handle detailed work or smaller projects.
Every method ensures a different texture and durability level, so selecting the right tool for the task can significantly impact the part’s longevity and performance in real-world conditions.
Routing Calculation
Routing calculation is an essential part of the manufacturing planning process, as it involves determining the sequence of operations needed to produce a part. This includes selecting the sequence of machining, polishing, and painting to ensure efficiency and high-quality output.
The concept of routing becomes crucial when multiple options exist for each stage of production. With three machining, four polishing, and three painting options available, combinatorics help in calculating the different possible routing scenarios. The formula used is a simple multiplication of available choices at each stage: \[3 \times 4 \times 3 = 36\]
This calculation is vital as it presents the different pathways a part can take in the manufacturing line. Understanding this keeps production flexible and can optimize both resources and time, allowing for smooth operation even if some equipment is unavailable or if a specific production method needs to be prioritized.

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