Question

Q 4: The 21,000-seat Air East Arena houses the local professional ice hockey, basketball, indoor soccer, and arena football teams as well as various trade shows, wrestling, and boxing matches, tractor pulls, and circuses. Arena vending annually sells large quantities of soft drinks and beer in plastic cups with the name of the arena and the various teams’ logos on them. The local container cup manufacturer that supplies the cups in boxes of 100 has offered arena management a discount price schedule for cups shown in table below. The annual demand for cups is 2.3 million, the annual carrying cost per box of cups is 5% of the price of the box of cups, and the ordering cost is $320. Determine the optimal order quantity, the length of the ordering cycle and total annual cost of the optimal ordering policy.

Order Quantity (Boxes)	Price per Box
2000-6,999 7000-11,999 12,000-19,999 20,000+	$47 $43 $41 $38

Answer 1

The optimal order quantity for order quantity between 2000 - 6999 units

EOQ =

EOQ =

EOQ = 25,028 units

Total cost = Ordering cost + holding cost + purchase cost

Total cost = ( 2,300,000 / 25,028 ) * $ 320 + ( 25,028/2) * 0.05 x $ 47 + $ 47 x 25,028

Total cost = $ 1,235,130.96

________________________________________________

The optimal order quantity for order quantity between 7000 - 11999 units

EOQ =

EOQ = 26,166

Total cost = ( 2,300,000 / 26,166 ) * $ 320 + ( 26,166/2) * 0.05 x $ 43 + $ 43 x 26,166

Total cost = $ 1,181,394.56

__________________________________

The optimal order quantity for order quantity between 12,000 - 19999 units

EOQ =

EOQ = 26,796

Total cost = ( 2,300,000 / 26796 ) * $ 320 + ( 26,796/2) * 0.05 x $ 41 + $ 41 x 26,796

Total cost = $ 1,153,568.69

_____________________________

The optimal order quantity for order quantity between 20,000 +

EOQ =

EOQ = 27,834

Total cost = ( 2,300,000 / 27,834 ) * $ 320 + ( 27,834/2) * 0.05 x $ 38 + $ 38 x 27,834

Total cost = $ 1,110,576.78

________________________________________

Thus the optimal order quantity is 27,834 units,

Length of order cycle = (Q/D) * 365

Length of order cycle = (  27,834 / 2,300,000 ) * 365

Length of order cycle = 4.42 days

Total annual cost of the optimal ordering policy = ( 2,300,000 / 27,834 ) * $ 320 + ( 27,834/2) * 0.05 x $ 38 + $ 38 x 27,834

Total annual cost of the optimal ordering policy =  $ 1,110,576.78