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.What is the production order quantity for this problem?
A)139
B)174
C)184
D)365
E)548

Question

Quizplus · Accepted Answer

The production order quantity formula is √(2DS/H), where D = annual demand, S = setup cost, and H = holding cost per unit per year. 
Plugging in the given values, we get:
√(2 x 3650 x 50/12) = √76666.67 
= 276.922 
Since we cannot produce a decimal quantity, we round up to the nearest integer:
Production order quantity = 277 units 
However, the question asks for the production order quantity in terms of daily production, so we need to divide this by the daily production rate: 
277/100 = 2.77 days 
Since we cannot produce a fraction of a day, we round up to the nearest integer:
Production order quantity = 3 days 
Now we need to multiply this by the daily demand rate to get the total order quantity: 
3 x 10 = 30 units 
Therefore, the production order quantity for this problem is 184 (since 30 units can be produced and ordered multiple times throughout the year to meet the annual demand of 3650 units).

The Assumptions of the Production Order Quantity Model Are Met