Question #206739

The company ABC produces travelling leather bags sold at the price of 120$ each, thus realising revenues from bags sales in amount of 1.680.000$. The CEO highlighted the problem of inventory management, especially the problem of high inventory costs if leather as a basic raw material. For each bag 1.25 squared meter of leather is used. The price of the leather is 50$ per 1square meter. The purchase department manager reported that the annual carrying cost per 1square meter of leather is 10% of the value, while the ordering costs per order have increased to 120$ per order. So far they have made equal orders every two months (60days), but now the company Board asked the OPTIMAL ordering quantity to be made, so to minimize the total inventory costs for the leather.

a)an optimal quantity of leather in square meters and compare with the current one

b) compare the total inventory cost that the company will pay if they plays current order, with the leather inventory costs for placing optimal order.

Expert's answer

The Economic order quantity is the optimal order quantity.

EOQ minimizes total costs(Ordering cost, receiving cost, and Inventory carrying cost)

A)

The formula for economic order quantity is

"Q=\\frac{(\\sqrt2 \\times Annual\\space Demand \\times ordering\\space cost\\space per\\space purchase \\space order)}{(Holding \\space costs\\space per \\space unit \\space per \\space year)}"

"Annual Demand=\\frac{\\$1,680,000}{\\$120}=14,000 bags X 1.25 \\space squared\\space meter \\space per \\space bag" =17,500 squared meter of leather

Ordering cost per purchase order=$120

Holding costs per unit per year=10% of $50=$5

"Q=\\frac{(\\sqrt{2} \\times 17,500 \\times \\$120)}{(\\$5)}=916 units"

B)

Annual ordering cost = Number of orders placed in a year x Cost per order

"No \\space of \\space order=\\frac{Annual\\space Demand}{EOQ}=\\frac{17,500}{916}=19.1"

"Ordering\\space Cost=19.1 \\times\\$120=\\$2292"

Annual holding cost = Average inventory level x Holding cost per unit per year

"=\\frac{ order \\space quantity}{2} \\times" Holding cost per unit per year

"=\\frac{916}{2} \\times \\$5=\\$2290"

Purchase Cost=17,500 sq.meter of leather X $50=$875,000

Total Cost=Purchase Cost+ Ordering Cost+ Annual Holding Cost=$875,000+$2,292+$2,290=$879,582

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