Question

A dealer has to supply his customer with 400 units of a product per week. The dealer gets the product from the manufacturer at a cost of ₹ 50 per unit. The cost of ordering from the manufacturers in ₹ 75 per order. The cost of holding inventory is 7.5 % per year of the product cost. Find

1. EOQ
2. Total optimum cost.

Answer 1

Demand = 400 units per week

Annual demand = 400 × 52 per year

Ordering cost per order C₃ = 175

Inventory cost C₁ = 7.5% per year of the cost

= 7.5% of 50 per year

`= 7.5/100 xx 50`

`= (7.5 xx 50)/(100 xx 52)` (per week)

(i) EOQ in units

EOQ = `sqrt((2"RC"_3)/"C"_1)`

`= sqrt((2 xx 400 xx 52 xx 75)/(7.5/100 xx 50))`

`= sqrt((2 xx 400 xx 52 xx 75 xx 100)/(7.5 xx 50))`

`= sqrt((2 xx 400 xx 52 xx 75 xx 100 xx 10)/(75 xx 50))`

`= sqrt(832000)`

= 912 (appr)

EOQ = 912 units

(ii) Total optimum cost = Purchasing cost + Minimum annual cost

`= 400 xx 50 + sqrt(2"RC"_3"C"_1)`

`= 20000 + sqrt(2 xx 400 xx 75 xx 7.5/(100 xx 52) xx 50)`

`= 20000 + sqrt(2 xx 4 xx 75 xx 7.5/52 xx 50)`

`= 20000 + sqrt((225000)/52)`

= 20000 +`sqrt 4326.92307`

= 20000 + `sqrt4326.9231`

= 20000 + 65.7793

= ₹ 20,065.78 per week