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In: Operations Management

For an inventory model - no backorder is allowed: D=16,428 ordering cost/order=517 Interest rate=0.27 Purchase price...

For an inventory model - no backorder is allowed:

D=16,428

ordering cost/order=517

Interest rate=0.27

Purchase price per item = 20

Calculate the unit costs?

Solutions

Expert Solution

Answer: As no specific information is mentioned in the question, we will find the unit cost by dividing the total inventory cost by the annual demand, assuming the total inventory cost includes, the annual inventory holding cost, annual inventory ordering cost, and the annual purchasing cost.

Step 1: Find Economic Order Quantity (EOQ)

Let D = Annual Demand = 16428 Units

O = Ordering Cost Per Order = 517 $

H = Holding Cost Per Unit Per Annum = 0.27 X 20 = 5.4 $

P = Purchase Price Per Unit = 20 $

Q = EOQ = SQRT [( 2 X D X O) / H]

= SQRT [ ( 2 X 16428 X 517) / 5.4]

= SQRT ( 3145657.78)

= 1773.60 Units (Rounded to 2 decimal places)

Step 2: Find the total inventory cost =

Total Inventory Cost = ( Q / 2) H + (D / Q) O + P X D

= [(1773.60 / 2 ) 5.4 ]+ [(16428 / 1773.60) 517] + [20 X 16428]

= 4788.72 + 4788.72 + 328560

= 338137.44 $

Step 3: Find Unit Cost

Unit Cost = Total Inventory Cost / D = 338137.44 / 16428 = 20.5830 $ (Rounded to 4 Decimal Places)

keosha answered 2 years ago
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