Shoe Shine is a local retail shoe store located on the north side of Centerville

Question

Shoe Shine is a local retail shoe store located on the north side of Centerville. Annual demand for a popular sandal is 500 pairs, and John Dirk, the owner of Shoe Shine, has been in the habit of ordering 100 pairs at a time. John estimates that the ordering cost is $10 per order. The cost of the sandal is $5 per pair.

1. If the carry cost were 10% of the cost, then the optimal order quantity would be _______ pairs of sandal.

2. If the optimal order quantity were 100 pairs of sandal, the carry cost should be _______ percent of the cost.

Explanation / Answer

Solution -

1. If the carry cost were 10% of the cost, then the optimal order quantity would be _______ pairs of sandal.

Ans - Here we need to calculate the optimal order quantity AKA Economic order Quantity for which the formula is as below

EOQ = SquareRoot [ 2 x A x O / C ]

where A = Annual demand or Annual consumption = 500

O = ordering cost per order = 10

C = Carrying Cost or Storage Cost per unit = 0.50 ( 5 x 10% - Cost per unit x carrying cost % of cost )

EOQ = Square Root [2 x 500 x 10 / 0.50 ]

EOQ = Square Root [10000 / 0.50 ]

EOQ = Square Root [20000 ]

EOQ = 141.4214

Thus optimal order quantity would be 141 pairs of sandal

2. If the optimal order quantity were 100 pairs of sandal, the carry cost should be _______ percent of the cost.

amending the same formula we can find the the carry cost

EOQ = SquareRoot [ 2 x A x O / C ]

Square EOQ   = 2 x A x O / C                           -----------------Applying Square both side

C = 2 x A x O / Square EOQ

C = 2 x 500 x 10 / Square (100 )

C = 10000 / 10000

C = $1

Thus the carrying cost has to be $1

However it is asked in % of Cost Price so 1/5 ie 20% of the cost price

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