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QUESTION

In an EOQ system, the actual parameters are:

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{$d=3000$ parts per year,\hspace{0.1in} $h=$\pounds3 per part per
year,\hspace{0.1in} $s=$\pounds125.}

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However, the decision-maker uses the following estimates:



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$d=3000$ parts per year,\hspace{0.1in} $h=$\pounds2 per part per
year,\hspace{0.1in} $s=$\pounds150.

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\item[(a)]
  What will the decision-maker decide and what is the
(actual) cost?
\item[(b)]
  By what percentage would the cost decrease if the actual
parameters were used?

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ANSWER

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\item[(a)]
The decision maker uses
$Q=\sqrt{\frac{2sd}{h}}=\sqrt{\frac{2.150.3000}{2}}=670.82$

The cost (using actual parameters) is

$$K=\frac{sd}{Q}+\frac{1}{2}hQ=\frac{125.3000}{670.82}+\frac{3}{2}.670.82=\pounds1565.25$$

\item[(b)]
With the actual parameters $Q=\sqrt{\frac{2.125.3000}{3}}=500$
with cost

$K=\frac{125.3000}{500}+\frac{3}{2}.500=\pounds15000.00$

Decrease in cost as a
percentage$=\frac{65.25}{1565.25}\times100=4.17\%$

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