A wholesaling business purchases an item from a manufacturer at a cost of $50 pe

Question

A wholesaling business purchases an item from a manufacturer at a cost of $50 per unit. On average, the business sells 12,500 units of this item each year to retailers. It costs the wholesaler $22 per order to process a purchase transaction and receive its shipment. The annual inventory carrying cost per unit for the item is 40% of its purchase cost per unit. Using the Basic Economic Order Quantity model, what is the EOQ for this item? Round answer to 1 decimal. 5 points How many orders per year will be placed for this item? Round answer to 1 decimal. 5 points What will the average inventory amount be for this item? Round answer to 1 decimal. 5 points What is the total annual cost if we order in Basic EOQ amounts? Round cost to a whole dollar amount. 5 points

Explanation / Answer

Here, we have

Annual demand D= 12,500 unit

Ordering cost S = $ 22 per order

Cost of Purchase P = $ 50 per Unit

Carrying cost H = 40% of cost of purchase = $ 50 * 40% = $ 20 per unit per annum

now calculate the followings -

a. Order quantity to minimize the cost is EOQ

EOQ = sqrt (2* D*S/H) = sqrt(2*12,500*22/20) = 165.83 units

b. optimal number of order per year = annual demand / EOQ = 12,500/165.83 = 75.38 orders

c. average inventory level = Q / 2 = 165.83 /2 = 82.92 units

Where Q = EOQ = 165.83 units

d. Annual total cost = total ordering cost + total carrying cost

= (D/Q)* S + (H*Q)/2 = (12,500/165.83)*22 + (20*165.83)/2 = $3,317

Here EOQ = Q = 165.83 units

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