The cost to set up for producing a standard component is approximately $300. Onc

ID: 364204 • Letter: T

Question

The cost to set up for producing a standard component is approximately $300. Once set up

they can produce at a rate of approximately 20 units/day (5,000 units per year) at a cost of $100 each.

Annual demand is forecast at 2,000 units. If the firm uses 30% annual rate for holding inventory:

What is the most economical lot size to produce(ERL)?

a. 200 b. 258.2 c. 1,000 d. 346.41 e. None

What is the average inventory level (units) ?

a. 77.46 b. 100 c. 129.1 d. 154.92 e. None

. What is the level of inventory (i.e., the proportion of production that goes into inventory)?

a. 0.25 b. 0.4 c. 0.6 d. 0.75 e. None

. What is the total inventory carrying costs ?

a. $1,080 b. $2,323.80 c. $3,873 d. $7,746 e. None

. What is the total number of days spent for production?

a. 2.5 days b. 10 days c. 12.91 days d. 50 days e. None

D = annual demand = 2000 units per year
S = setup cost = $300
H = inventory holding cost = 30% x $100 = $30
P = production rate = 5000 units per year

Economic Lot Size = (2.D.S / H)1/2 x (P / (P - D))1/2 = sqrt(2*2000*300/30)*sqrt(5000/(5000-2000)) = 258.2

Average inventory level = (ERL / 2) x (P - D) / P = (258.2/2)*(5000-2000)/5000 = 77.46

Inventory level = (P - D) / P = (5000 - 2000) / 5000 = 0.60

Total carrying cost = Average inventory level x H = 77.46 x 30 = $2,323.80

Number of days spent for production (of one lot) = ERL / rate of production = 258.2 / 20 = 12.91 days

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