A product has a demand of 4000 units per year. ordering cost is $20, and holding cost is $4 per unit per year. the eoq model is appropriate. the cost-minimizing solution for this product will cost ________ per year in total annual inventory (holding and setup) costs.

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)

To determine 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)

To determine 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

=([(2 ¡Á6,000 ¡Á30)/(10)])

=189.736 ¡Ö 189.74 units

Hence, EOQ = 189.74 units

Explanation:

A)

To 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)

To determine 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)

To determine 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

=([(2 ¡Á6,000 ¡Á30)/(10)])

=189.736 ¡Ö 189.74 units

Hence, EOQ = 189.74 units

B)

Average inventory level = (Order Quantity/2)

= (189.74) /2

= 94.87

Average Inventory level =94.87 units

C)

N= ( Demand/ order quantity)

= (6000/ 189.736)

=31.62

Hence, the optimal number of orders per year = 31.62

D)

T = (Number of Working Days per year) / (optimal number of orders)

= 250 days per year / 31.62

= 7.906

So, the optimal number of days in between any two orders = 7.91

E)

Using, (Q) x (H) : (189.736 units) x ($10) =$1,897.36

So, The annual cost of ordering and holding the inventory = $1,897

F)

TC = setup cost + holding cost

= (Dyear/Q) (S) + (Q/2) (H)

= (6,000/189.74) ($30.00) + (189.74/2) ($10.00)

= $948.67 + $948.7

= 1,897.37

Purchase cost = (6,000 units) x ($100/unit)

= $600,000

Total annual inventory cost = $600,000 + $1,897

= $601,897