Problem 2: Quantity Discounts (5 points) The hospital also buys plasma for use i
ID: 452019 • Letter: P
Question
Problem 2: Quantity Discounts (5 points)
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.
1. What is the economic order quantity? (2 points)
2. 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 if101 or more units of plasma are ordered the unit price is $59.55.
3. What order quantity will result in the lowest total annual cost for the hospital? Be sure to show your work for full credit. (3 points)
Explanation / Answer
(a)Economic Order Quantity = sqrt( 2 * D * S / H)
where: D = annual demand for plasma = 2,028 units per year
S is order cost = $ 40 per order
H is holding cost = $ 60
Now EOQ = sqrt ((2 * 2028 * 40)/60 ) = 52 units
(b) Total cost TC = Q/2 * H + SD/Q
where
TC is the total cost = ?
D is the total number of units purchased in a year = 2028 units.
H is the holding cost per unit per year =$60 per unit per annum.
Q is the quantity ordered each time an order is placed= 52 units per order.
S is the fixed cost of each order $ 40 per order.
The above calculation is done with different order quantity, the Lowest total annual cost for the hospital is at the EOQ = 52 units. The Quantity between 25 - 75 at the price od $ 59.89 per unit.
D 2028 S 40 H 60 order quantity (Q) Price per unit Q *H/2 D*S/Q Total Cost 25 60 750 3244.8 3994.8 52 59.85 1560 1560 3120 75 59.85 2250 1081.6 3331.6 100 59.7 3000 811.2 3811.2 125 59.55 3750 648.96 4398.96Related Questions
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