A company manufactures 1,200 cylinders per day, each requiring a pressure gauge. The purchase price of the pressure gauge is $3.20. The company controller estimated annual holding costs at 25 percent per year, while the cost of placing an order was estimated at $55.00. Assuming that the plant operates 45 weeks per year, the EOQ for the pressure gauge is:

a.3,000 units
b.2,929 units.
c.2,872 units.
d.2,725 units.
e.1,200 units.

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

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