Suad Alwan, The Purchasing Agent For Dubai Airlines, Has Determined That The Third Plane Took 16,000 Hours To Produce. Using A 75 % 75\% 75% Learning Curve And A $ 30 \$30 $30 -per-hour Labor Charge, He Wants To Determine The Cost Of The Six

Introduction

In the world of manufacturing and production, understanding the learning curve is crucial for determining the cost of producing a product. The learning curve is a mathematical concept that describes how the cost of producing a product decreases as the number of units produced increases. In this article, we will explore the concept of the learning curve and how it can be used to determine the cost of producing a product.

What is the Learning Curve?

The learning curve is a graphical representation of how the cost of producing a product decreases as the number of units produced increases. It is typically represented as a straight line on a graph, with the x-axis representing the number of units produced and the y-axis representing the cost per unit. The learning curve is often expressed as a percentage, with a higher percentage indicating a steeper learning curve.

The Formula for the Learning Curve

The formula for the learning curve is given by:

C = C0 * (N0/N)^(b)

Where:

• C is the cost per unit at a given production level
• C0 is the cost per unit at the initial production level
• N is the current production level
• N0 is the initial production level
• b is the learning curve exponent

Applying the Learning Curve to the Problem

In the problem presented, Suad Alwan, the purchasing agent for Dubai Airlines, has determined that the third plane took 16,000 hours to produce. Using a $75\%$ learning curve and a $\$30$-per-hour labor charge, he wants to determine the cost of the six planes.

To solve this problem, we need to first determine the cost per unit at the initial production level. Let's assume that the initial production level is the third plane, which took 16,000 hours to produce. The cost per unit at this level is given by:

C0 = Labor charge per hour * Number of hours to produce the third plane = $30/hour * 16,000 hours = $480,000

Calculating the Cost of the Six Planes

Now that we have determined the cost per unit at the initial production level, we can use the learning curve formula to calculate the cost of the six planes.

First, we need to determine the learning curve exponent (b). Since the learning curve is $75\%$, we can express it as:

b = 1 - (1/0.75) = 1 - 1.3333 = -0.3333

Now, we can plug in the values into the learning curve formula:

C = C0 * (N0/N)^(b) = $480,000 * (3/6)^(-0.3333) = $480,000 * (0.5)^(-0.3333) = $480,000 * 1.1487 = $551,116

Conclusion

In this article, we have explored the concept of the learning curve and how it can be used to determine the cost of producing a product. We have applied the learning curve formula to a real-world problem and calculated the cost of producing six planes using a $75\%$ learning curve and a $\$30$-per-hour labor charge. The result shows that the cost of producing the six planes is approximately $551,116.

References

• [1] "Learning Curve" by Wikipedia
• [2] "Learning Curve Formula" by Math Is Fun
• [3] "Learning Curve in Manufacturing" by IndustryWeek

Additional Resources

• [1] "Learning Curve Calculator" by Calculator Soup
• [2] "Learning Curve Formula Excel" by Excel-Easy
• [3] "Learning Curve in Project Management" by Project Management Institute
  Learning Curve Q&A: Understanding the Concept and Its Applications ====================================================================

Introduction

In our previous article, we explored the concept of the learning curve and how it can be used to determine the cost of producing a product. In this article, we will answer some frequently asked questions about the learning curve and its applications.

Q: What is the learning curve?

A: The learning curve is a graphical representation of how the cost of producing a product decreases as the number of units produced increases. It is typically represented as a straight line on a graph, with the x-axis representing the number of units produced and the y-axis representing the cost per unit.

Q: What is the formula for the learning curve?

A: The formula for the learning curve is given by:

C = C0 * (N0/N)^(b)

Where:

• C is the cost per unit at a given production level
• C0 is the cost per unit at the initial production level
• N is the current production level
• N0 is the initial production level
• b is the learning curve exponent

Q: What is the learning curve exponent (b)?

A: The learning curve exponent (b) is a value that determines the steepness of the learning curve. A higher value of b indicates a steeper learning curve, while a lower value indicates a flatter learning curve.

Q: How do I determine the learning curve exponent (b)?

A: The learning curve exponent (b) can be determined using the following formula:

b = 1 - (1/0.75) = 1 - 1.3333 = -0.3333

Q: What is the difference between a 50% and a 75% learning curve?

A: A 50% learning curve indicates that the cost of producing a product decreases by 50% for every doubling of the production level. A 75% learning curve indicates that the cost of producing a product decreases by 75% for every doubling of the production level.

Q: Can I use the learning curve to determine the cost of producing a product with a different production level?

A: Yes, you can use the learning curve to determine the cost of producing a product with a different production level. Simply plug in the new production level into the learning curve formula and calculate the new cost per unit.

Q: What are some real-world applications of the learning curve?

A: The learning curve has many real-world applications, including:

• Manufacturing: The learning curve can be used to determine the cost of producing a product with a different production level.
• Project management: The learning curve can be used to determine the cost of completing a project with a different level of complexity.
• Economics: The learning curve can be used to determine the cost of producing a product with a different level of demand.

Q: How do I calculate the learning curve exponent (b) for a specific product?

A: To calculate the learning curve exponent (b) for a specific product, you will need to gather data on the cost of producing the product at different production levels. Once you have this data, you can use the following formula to calculate the learning curve exponent (b):

b = 1 - (1/0.75) = 1 - 1.3333 = -0.3333

Conclusion

In this article, we have answered some frequently asked questions about the learning curve and its applications. We have also provided some real-world examples of how the learning curve can be used to determine the cost of producing a product with a different production level.

References

• [1] "Learning Curve" by Wikipedia
• [2] "Learning Curve Formula" by Math Is Fun
• [3] "Learning Curve in Manufacturing" by IndustryWeek

Additional Resources

• [1] "Learning Curve Calculator" by Calculator Soup
• [2] "Learning Curve Formula Excel" by Excel-Easy
• [3] "Learning Curve in Project Management" by Project Management Institute