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ABC Manufacturing produces a product for which the monthly demand is 900 units. Production averages 100 units per day. Holding costs are $2.00 per unit per year, and setup cost is $200.00. the company operates 240 days per yeara. If the company wishes to produce this product in economic batches, what size batch should be used?b. What is the maximum inventory level? c. What is the average inventory? d. How many order cycles are there per year? e. What are the total cost of managing the inventory? $

Respuesta :

Answer:

EPQ =  1982  

maximum inventory =  1090

average inventory =  545

order cycles =  44.04

total cost of managing  =  $2180

Explanation:

given data

monthly demand = 900

annual demand = 12 × 900 = 10800

Production averages = 100 units

Holding costs = $2.00

setup cost = $200.00

company operates= 240 days

solution

daily usage = [tex]\frac{10800}{240}[/tex]

daily usage = 45

we find here EPQ

EPQ = [tex]\sqrt{\frac{2*demand*setucost}{holding cost}}[/tex] × [tex]\sqrt{\frac{daily production}{daily production - daily use}}[/tex]   ...........1

EPQ = [tex]\sqrt{\frac{2 * 10800 * 200}{2}}[/tex] × [tex]\sqrt{\frac{100}{100-45}}[/tex]

EPQ =  1982  

and

maximum inventory = [tex]\frac{Q}{daily production}[/tex] × daily production - daily use

maximum inventory = [tex]\frac{1982}{100}[/tex] × (100-45)

maximum inventory =  1090

and

average inventory = [tex]\frac{maximum inventory}{2}[/tex]

average inventory = [tex]\frac{1090}{2}[/tex]

average inventory =  545

and

order cycles =  [tex]\frac{Q}{daily use}[/tex]

order cycles =  [tex]\frac{1982}{45}[/tex]

order cycles =  44.04

and

total cost of managing  = [tex]\frac{maximum inventory}{2}* holding cost + \frac{demand}{Q}*setup cost[/tex]

total cost of managing  = [tex]\frac{1090}{2}* 2 + \frac{10800}{1982}*200[/tex]

total cost of managing  = 2179.81 = $2180