Aproduct 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.

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 

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