$\"\"$

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The cost function is $\"\"$ ,

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$\"\"$ is the ordering and transportation cost for components used, measured in thousands of dollars.

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$\"\"$ is the order size in hundreds.

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Find the rate of change of cost function.

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Quotient rule of derivatives : $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a)

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Find the rate of change of cost function at $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the above function.

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$\"\"$

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$\"\"$ thousand/ $\"\"$ components.

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$\"\"$

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(b)

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Find the rate of change of cost function at $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the above function.

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$\"\"$

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$\"\"$ thousand/ $\"\"$ components.

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$\"\"$

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(c)

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Find the rate of change of cost function at $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the above function.

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$\"\"$

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$\"\"$ thousand/ $\"\"$ components.

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Observe the value of $\"\"$ for different values of $\"\"$ .

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As the size of the order increases, rate of change in cost decreases.

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$\"\"$

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(a) $\"\"$ thousand/ $\"\"$ components.

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(b) $\"\"$ thousand/ $\"\"$ components.

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(c) $\"\"$ thousand/ $\"\"$ components.

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As the size of the order increases, rate of change in cost decreases.