Question

The mythical Three Floyds Brewery in Munster, Indiana makes a beer called Zombie Dust, which it sells in large bottles to pubs and stores in the Midwest. The setup cost of brewing and bottling a batch of beer is $1,800 per setup. The holding cost of storing a bottle of beer is $2.50 per year. The annual demand for Zombie Dust is 20,000 bottles. Three Floyds Brewery can brew and bottle beer at the rate of 400 bottles per day. The brewery operates 250 days per year and currently produces Zombie Dust in batches of 10,000 bottles.
a. What is the annual holding and setup cost of their current production schedule?
b. What is the economic production quantity (EPQ)?
c. What is the cost difference between the current production schedule and the EPQ?

Answer 1

Answer:

Setup cost (S) = 1800

Holding cost (H) = 2.5

Annual demand (D) = 20000

Daily demand (d) = Annual demand / Number of working days = 20000 bottles/250 = 80 bottles daily

Daily production (p) = 400

a. Given production quantity Q = 10000

Holding cost = 1/2*[(p-d)/p]*QH

Holding cost = ((400-80)/(2*400))*10000 *2.5= 10000

Ordering cost = (D/Q)S = (20000/10000)*1800 = 3600

Total Cost = Annual holding cost + Annual ordering Cost = 10000 + 3600 = 13600

b. Economic production Quantity (EPQ) = Q

Q = √2DS/H √p/p-d

Q = √2*20000*1800/2.5 √400 / 400-80

Q = 6000 bottles

Holding cost = 1/2*[(p-d)/p]*QH

Holding cost = ((400-80)/(2*400))*6000 *2.5= 6000

Ordering cost = (D/Q)S = (20000/6000)*1800 = 6000

Total Cost = Annual Holding cost + Annual ordering cost = 6000 + 6000 = 12000

C. Cost difference between the current production schedule and the EPQ = 13600 - 12000 = 1600