Quantity Discounts The hospital also buys plasma for use in surgical procedures.
ID: 452187 • Letter: Q
Question
Quantity Discounts The hospital also buys plasma for use in surgical procedures. The demand for plasma is 2,028 units per year. There is a $40 cost to place an order and the cost per unit of plasma to hold it in inventory for the year is $60. What is the economic order quantity? For part b) assume the cost of a unit of plasma is based on the quantity ordered at one time. If less than 25 units of plasma are ordered the unit price is $60; if 26-75 units of plasma are ordered the unit price is $59.85; if 76-100 units of plasma are ordered the unit price is $59.70; and if 101 or more units of plasma are ordered the unit price Is $59.55. What order quantity will result in the lowest total annual cost for the hospital? Be sure to show your work for full credit.Explanation / Answer
a. economic order quantity = (2*annual demand*order cost/holding cost)^0.5
annual demand = 2028 units per year. cost per order = $40 and holding cost = $60
economic order quantity = (2*2028*40/60)^0.5 = (162240/60)^0.5 = 2704^0.5 = 52 plasma.
b. Total cost = (order quantity/2)*carrying cost+(annual demand/order quantity)*ordering cost+price*annual demand
order cost and carrying cost are assumed to be the same as given in part "a" of the question:
The order brackets and the prices are:
(i) total cost @ optimal order quantity of 52: (52/2)*60 + (2028/52)*40 + 59.85*2028 (price for 52 plasmas will fall in the bracket of 26-75 units and price will be 59.85) = $124,495.8
(ii) total cost when order quantity is in the bracket 0-25, let's say 25: (25/2)*60 + (2028/25)*40 + 60*2028 = $125,674.8
(iii) Total cost when order quantity is in the bracket 76-100, let's say 76: (76/2)*60 + (2028/76)*40 + 59.7*2028 = $124,419
(iv) Total cost in the bracket >100, let's say 101: (101/2)*60 + (2028/101)*40 + 59.55*2028 = $124,600.6
The lowest cost is in the 3rd scenarion when the order quantity is 76 - 100. Thus the order quantity should be between 76 units to 100 units.
0-25 60 26-75 59.85 76-100 59.7 >100 59.55