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If EOQ can assist in reducing inventory levels, the cash savings can be utilized for another company's purpose or investment. However, as the amount of the inventory grows, so does the expense of storing the inventory. EOQ is the exact moment at which both of these inversely associated expenses are minimized. The EOQ Formula. By setting the first-order derivative to zero, the Economic Order Quantityformula is determined by reducing the overall cost per order.

Thus, the holding cost is 30 % of 0.80

$$\begin{gathered} \mathrm{EOQ}=\sqrt{\frac{2脳\mathrm{A}脳\mathrm{S}}{\mathrm{H}}} \\ \mathrm{where}, \\ \mathrm{A}=\mathrm{Annual}\mathrm{demand} \\ \mathrm{S}=\mathrm{Ordering}\mathrm{cost}\mathrm{per}\mathrm{unit} \\ \mathrm{H}=\mathrm{Carrying}\mathrm{cost}\mathrm{per}\mathrm{unit} \end{gathered}$$

$\begin{array}{rcl}\mathrm{EOQ}& =& \sqrt{\frac{2脳\mathrm{A}脳\mathrm{S}}{\mathrm{H}}}\\ & =& \sqrt{\frac{2脳51,000脳\$30}{0.24}}\\ & =& 3,571\mathrm{units}\end{array}$

$\begin{array}{rcl}Total\cos t& =& \frac{Annualdemand脳Ordering\cos t}{EOQ}+\frac{EOQ脳holding\cos t}{2}+\left(Sellingprice脳Annualdemand\right)\\ & =& \frac{51,000\$30}{3,571}+\frac{3,571脳\$0.24}{2}+\left(0.80脳51,000\right)\\ & =& \$428.45+\$428.52+\$40,800\\ & =& \$41,656.97\end{array}$(ii) If the price of copper is $0.79

Thus, the holding cost is 30% of 0.79 = $0.237

$\begin{array}{rcl}\mathrm{EOQ}& =& \sqrt{\frac{2脳\mathrm{A}脳\mathrm{S}}{\mathrm{H}}}\\ & =& \sqrt{\frac{2脳51,000脳\$30}{0.237}}\\ & =& 3,593\mathrm{units}\end{array}$

$\begin{array}{rcl}Total\cos t& =& \frac{Annualdemand脳Ordering\cos t}{EOQ}脳\frac{EOQ脳holding\cos t}{2}+\left(Sellingprice脳Annualdemand\right)\\ & =& \frac{51,000脳\$30}{3,593}+\frac{3,593脳\$0.237}{2}+\left(0.79脳51,000\right)\\ & =& \$425.82+\$425.77+\$40,290\\ & =& \$41,141.59\end{array}$

(iii) If the price of copper is $0.77.

Thus, the holding cost is 30 % of 0.77 = $ 0.231

$\begin{array}{rcl}\mathrm{EOQ}& =& \sqrt{\frac{2脳\mathrm{A}脳\mathrm{S}}{\mathrm{H}}}\\ & =& \sqrt{\frac{2脳51,000脳\$30}{0.231}}\\ & =& 3,640\mathrm{units}\end{array}$

$\begin{array}{rcl}Total\cos t& =& \frac{Annualdemand脳Ordering\cos t}{EOQ}+\frac{EOQ脳holding\cos t}{2}+\left(Sellingprice脳Annualdemand\right)\\ & =& \frac{51,000脳\$30}{3,640}+\frac{3,640脳\$0.231}{2}+\left(0.71脳51,000\right)\\ & =& \$420.32+\$420.42+\$39,270\\ & =& \$40,1100.74\end{array}$

Therefore, the lowest total cost is $ 40,110.74 with a selling price of $0.77 and the optimal order quantity should be 3,650 units and 5,000 pounds or greater should be ordered.