An auto parts shop carries an oil filter for trucks. The annual demand for the oil filter is roughly 1200 units. The ordering cost per order for the auto parts shop is $80; the holding cost of carrying 1 unit is $1.2 per year. The shop has 360 working days per year. The lead time is usually 12 working days. Determine the annual total relevant, including ordering and carrying, cost. a) 240
b) 80
c) 480
d) 300
e) None of the above.

Total annual inventory cost = $480

c) 480

Step-by-step explanation:

given data

annual demand for the oil filter = 1200 units

ordering cost per order S = $80

holding cost of carrying 1 unit = $1.2 per year

lead time = 12 working days

number of working days = 360 days

solution

we get here economic order quantity that is express as

economic order quantity =    ...............1

here D is annual demand and S is ordering cost and H is per unit cost

so put here value and we get

EOQ =  

EOQ = 400 units

and

Annual ordering cost = annual demand × ordering cost ÷ order size   .........2

and here

No orders (Q) = annual demand ÷ order size   ...........3

Q =  1200 ÷ 400

Q = 3 orders

so

Annual ordering cost = ordering cost × number of order  ................4

put here value

Annual ordering cost = 80 × 3

Annual ordering cost = $240

and

Annual carrying cost = average inventory × per unit cost    ..........5

and

average inventory = EOQ ÷ 2        ...........6

Annual carrying cost = (EOQ × H) ÷ 2

put here value and we get

Annual carrying cost = 400 × 1.2  ÷ 2

Annual carrying cost = $240

and

so here Total annual inventory cost = Annual ordering cost + Annual carrying cost    .........................7

Total annual inventory cost = $240 + $240)

Total annual inventory cost = $480