Answer:
a) Order size= 20,000 units
b) No of orders= 5.
Annual ordering cost = $50
c) Average inventory = 10,000 units
Annual holding cost= $50
Explanation:
To minimize total inventory cost, the company would have to place order equal to the Economic Order Quantity(EOQ)
EOQ = √2× Co× D/Ch
EOQ - economic order quantity , Co- ordering cost per order, Ch- carrying cost per unit per year, D- Annual demand
EOQ =√ (2× 10× 100,000)/0.005= 20,000 units
No of orders to place = Annual demand/EOQ
= 100,000/ 20,000
= 5 orders
Annual ordering cost = 5 × $10 = $50
Average inventory = Minimum stock + order quantity/2
= 20,000/2 = 10,000 units
Annual holding cost = average inventory × holding cost per unit
= 10,000 × 0.005= $50
Order size= 20,000 units
No of orders= 5.
Annual ordering cost = $50
Average inventory = 10,000 units
Annual holding cost= $50
The order quantity that will minimize the total inventory cost (EOQ) will be 20,000 screws. The number of orders will be 5, the annual ordering cost will be $50, the average inventory will be 10,000 and the annual holding cost is $50.
The EOQ or Economic Order Quantity is the optimal order quantity that results in minimized total cost. The EOQ helps the company to decide a purchase quantity that will minimize its holding and ordering costs.
The formula to calculate EOQ is:
[tex]\rm EOQ = \sqrt{\dfrac{2AO}{HC}[/tex], where A is the annual demand, O is the ordering cost, and HC is the holding cost of the material.
a. The number 6 screws that should be ordered to minimize total inventory cost is the EOQ and will be calculated as follows:
Given,
[tex]\rm A = 100,000\\\\O = \$10\\\\HC = \dfrac{1}{2} \: \rm of \:1\:cent[/tex]
We know that,
[tex]\rm 1\:cent = \$\dfrac{1}{100}[/tex]
Holding cost will be:
[tex]\rm HC = \$\dfrac{1}{100} \times \dfrac{1}{2}\\\\HC = \$0.005[/tex]
Therefore the EOQ will be:
[tex]\rm EOQ = \sqrt{\dfrac{2AO}{HC}\\\\\\\\\rm EOQ = \sqrt{\dfrac{2(100,000)(10)}{0.005}\\\\\rm EOQ = \sqrt{\dfrac{2,000,000}{0.005}\\\\\rm EOQ = \sqrt{400,000,000\\\\\\\\\rm EOQ = 20,000[/tex]
b. The number of orders will be calculated as:
[tex]\rm Number\:of\:orders = \dfrac{Annual\:Demand}{EOQ}\\\\\rm Number\:of\:orders = \dfrac{100,000}{20,000}\\\\\rm Number\:of\:orders =5[/tex]
The annual ordering cost will be:
[tex]\rm Annual \:ordering\: cost = Number\:of\:orders \:x\: Ordering\:cost\:per\:order\\\\\rm Annual \:ordering\: cost = 5\:x\:10\\\\\rm Annual \:ordering\: cost = \$50[/tex]
c. Average inventory will be calculated as:
[tex]\rm Average\:inventory = \dfrac{EOQ}{2}\\\\\rm Average\:inventory = \dfrac{20,000}{2}\\\\\rm Average\:inventory = 10,000[/tex]
The annual holding cost will be:
[tex]\rm Annual \:holding\:cost = Average\:inventory\:x\: Holding\:cost\:per\:screw\\\\\rm Annual \:holding\:cost = 10,000\:x\:0.005\\\\\rm Annual \:holding\:cost = \$50[/tex]
Therefore the answers are;
[tex]\begin{aligned} \rm EOQ &= 20,000\\\\Number\:of\:orders &= 5\\\\Annual\:ordering\:cost &= \$50\\\\Average\:inventory &= 10,000\\\\Annual \:holding\:cost &= $50\end[/tex]
Learn more about EOQ, carrying cost, and holding cost here:
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