a. What is the EOQ? = 189.74 units
Step (1): Determine the Annual Set-up Cost
*Annual set-up cost = (# of orders placed per year) x (Setup or order cost per order)
= Annual Demand
# of units in each order ¡Á (Setup or order cost per order)
= (D/Q) ¡Á(S)
= (6000/Q) x (30)
Step (2): Annual holding cost = Average inventory level x Holding cost per unit per year
= (Order Quantity/2) (Holding cost per unit per year)
= (Q/2) ($10.00)
Optimal order quantity is found when annual setup cost equals annual holding cost:
(D/Q) x (S) = (Q/2) x (H)
(6,000/Q) x (30) = (Q/2) (10)
=(2)(6,000)(30) = Q2 (10)
Q2 = [(2 ¡Á6,000 ¡Á30)/($10)] = 36,000
Q = ¡Ì([(2 ¡Á6,000 ¡Á30)/(10)]) = ¡Ì36,000
Q = 189.736 ¡Ö 189.74 units
EOQ = 189.74 units
b. What is the average inventory if the EOQ is used?
Average inventory level = (Order Quantity/2)
= (189.74) /2 = 94.87
Average Inventory level =94.87 units
c. What is the optimal number of orders per year?
N= ( Demand/ order quantity) = (6000/ 189.736)=31.62
N = 31.62
The optimal number of orders per year = 31.62
d. What is the optimal number of days in between any two orders?
T = (Number of Working Days per year) / (optimal number of orders)
T = 250 days per year / 31.62 = 7.906
The optimal number of days in between any two orders = 7.91
e. What is the annual cost of ordering and holding inventory?
(Q) x (H)
(189.736 units) x ($10) =$1,897.36
The annual cost of ordering and holding the inventory = $1,897
f. What is the total annual inventory cost, including cost of the 6,000 units?
TC = setup cost + holding cost
TC = (Dyear/Q) (S) + (Q/2) (H)
TC = (6,000/189.74) ($30.00) + (189.74/2) ($10.00)
TC = $948.67 + $948.7
TC = 1,897.37 ¡Ö $1,897
Purchase cost = (6,000 units) x ($100/unit) = $600,000
Total annual inventory cost = $600,000 + $1,897 = $601,897
Total annual inventory cost = $601,897
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