Question

CU, Incorporated, (CUI) produces copper contacts that it uses in switches and relays. CUI needs to determine the order quantity, Q, to meet the annual demand at the lowest cost. The price of copper depends on the quantity ordered. Here are price-break and other data for the problem:

Price of copper	\(0.82 per pound up to 2,499 pounds \)0.81 per pound for orders between 2,500 and 5,000 pounds \(0.80 per pound for orders greater than 5,000 pounds
Annual demand	50,000 pounds per year
Holding cost	20 percent per unit per year of the price of the copper
Ordering cost	\)30

Which quantity should be ordered?

Short answer

Answer

Economic order quantity (EOQ) is the optimal quantity of inventory that a corporation should acquire given a fixed cost of production, a fixed demand rate, and other factors.

Step-by-step solution

Economic order quantity (EOQ)

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.

The calculations of Economic order quantity (EOQ) for the company are as follows

(i) If the price of copper is $ 0.80

Thus, the holding cost is 30 % of 0.80

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

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

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

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

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

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

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

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

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

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

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.