The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units, setup cost is $50, holding cost is $12 per unit per year, the daily demand rate is 10 and the daily production rate is 100. The production order quantity for this problem is approximately
A) 139
B) 174
C) 184
D) 365
E) 548

Question

Quizplus · Accepted Answer

The production order quantity formula is:

$Q=\sqrt{\frac{2DS}{H}}$

where 
D = annual demand
S = setup cost
H = holding cost per unit per year

In this case, 
D = 3650 units
S = $50
H = $12 per unit per year

We need to convert the annual demand to daily demand by dividing by the number of working days in a year, assuming that demand is uniform throughout the year:

Daily demand = Annual demand / number of working days
= 3650 / 250 (assuming 250 working days in a year)
= 14.6 units per day

The production rate is given as 100 units per day, so we have:

$Q=\sqrt{\frac{2	imes 14.6	imes 50}{12}}$
= 183.9

Rounding up to the nearest integer, we have:

Answer: C, 184

The Assumptions of the Production Order Quantity Model Are Met