Answer:
Option D is correct.
Economic order quantity = 2725 units.
Explanation:
We will use the following variables:
Q = Quantity ordered/made
EOQ = the optimal order Quantity
D = annual Demand over the year
P = unit Production cost
S = cost of setting up a production run, regardless of the number of units in the production run (fixed cost per production run), also the ordering cost for goods that are usually ordered.
H = cost to Hold one unit for a year in the warehouse.
It is important to note which variables are based on per-order and per-unit basis.
Total Cost, TC = PC + SC + HC
PC = P x D : Production Cost = unit Production cost × the annual Demand
SC = (D x S)/Q : Setting up Cost = (annual Demand) × (cost per production setup)/(Order Quantity)
HC = (H x Q)/2: Holding Cost = (annual unit Holding cost × order Quantity)/2 (it ks divided by 2 because throughout the year, the warehouse is half full on average).
So TC = PC + SC + HC = (P x D) + ((D x S)/Q) + ((H x Q)/2) = PD + (DS/Q) + HQ/2
To obtain the optimal order quantity, EOQ, that minimizes TC, at the minimum TC, dTC/dQ = 0
dTC/dQ = (H/2) – (D x S)/(Q²) = 0
(H/2) – (D x S)/(Q²) = 0
Solving for Q, which is EOQ at this point.
(EOQ)² = 2DS/H
EOQ = √(2DS/H)
D = annual Demand for the item, over the year = 1200 × 45 = 54000 units
S = cost of setting up a production run, regardless of the number of units in the production run (fixed cost per production run) or for one order = $55
H = Holding cost = 25% of $3.2 = $0.8
EOQ = √(2×54000×55/0.8) = 2725 units
