If a factory wants to cut its current lot size in half, by what proportion must setup cost change?

 Options:

A. Setup cost must be cut to one fourth its current value. B. Setup cost must also be cut in half from its current value. C. Setup cost must double from its current value. D. Cannot be determined. E. Setup cost must quadruple from its current value.

The Correct Answer Is:

A. Setup cost must be cut to one fourth its current value.

Correct Answer Explanation: A. Setup cost must be cut to one fourth its current value.

The correct answer is A. Setup cost must be cut to one fourth its current value. Let’s delve into the reasoning behind this choice and then explore why the other options are not correct.

When a factory decides to cut its current lot size in half, it implies that the production runs will be smaller, resulting in more frequent setups. Setup costs are typically associated with preparing a machine or a production line for a specific manufacturing process.

If the lot size is reduced, the number of setups will increase, leading to a potential increase in setup costs. To offset this increase and maintain cost efficiency, the setup cost must be reduced proportionally.

Now, let’s break down the other options:

B. Setup cost must also be cut in half from its current value:

This option suggests a direct correlation between the reduction in lot size and an equal reduction in setup costs. However, the relationship between lot size and setup costs is more complex than a simple one-to-one correlation. While reducing the lot size may necessitate more frequent setups, the cost reduction might not align proportionally.

Setup costs involve various elements, including labor, time, resources, and machine preparation, which may not reduce linearly with smaller lot sizes. Therefore, assuming an exact halving of setup costs alongside a halving of lot sizes oversimplifies the situation and doesn’t reflect the actual cost dynamics accurately.

C. Setup cost must double from its current value:

This option implies that reducing lot size by half will result in a doubling of setup costs. However, this assumption greatly overestimates the impact of lot size reduction on setup costs. Doubling the setup costs would far exceed the necessary adjustment needed to accommodate smaller lot sizes.

In reality, while smaller lot sizes might lead to increased setup frequency, the corresponding increase in setup costs is unlikely to be as drastic as doubling.

D. Cannot be determined:

This option assumes that there isn’t enough information available to make a conclusive determination about the relationship between lot size and setup costs. However, in manufacturing and operations management, there’s a known relationship between these variables, even if the exact formula might vary based on specific circumstances.

While the precise calculation might depend on various factors such as production processes, machinery, and workforce, the basic understanding that reducing lot size necessitates adjustments in setup costs is a fundamental principle in manufacturing.

E. Setup cost must quadruple from its current value:

Similar to option C, this option overestimates the impact of lot size reduction on setup costs. Quadrupling the setup costs would represent a significant exaggeration of the necessary adjustment needed to accommodate smaller lot sizes.

It assumes an extreme increase in setup costs that is not justified by the reduction in lot size alone.

In summary, each of these options either oversimplifies or overestimates the relationship between lot size reduction and setup costs. Option A remains the most reasonable choice, as it accurately reflects the need for a proportional reduction in setup costs to maintain cost efficiency when halving the lot size.

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