Question

Financial management.

Thika filters Company is a distributor of air filters to retail stores. It buys its filters from severalmanufacturers. Filters are ordered in lot sizes of 1,000 and each order costs Kshs. 40 to place.Demand from the retail stores is 20,000 filters per month and carrying cost is Kshs. 0.10 a filterper month.

(i) What is optimal filter order quantity in lot sizes of 1,000
(ii) What would be the optimal order quantity if the carrying costs were cut I half to Kes.0.05 afilter per month.
(iii)What would be the optimal order quantity if ordering costs were reduced to Kshs. 10 perorder.

Answer 1

Economic Order Quantity (EOQ) EOQ

=(2 × Annual demand × ordering cost per order/carrying cost per annum)^1/2

(i)

• Annual demand = 20,000 filters × 12 = 240,000 filters
• Ordering cost per order = $40
• Carrying cost per unit per annum = $0.10 × 12 = $1.2

Optimal filter order quantity =

=(2 × 240,000 × 40 /1.2)^1/2

= (19,200,000/1.2)^1/2

=(16,000,000)^1/2

= 4,000

The optimal filter order quantity is 4,000 filters

The optimal filter order quantity in lot sizes of 1,000 =

4,000/1,000 = 4

(ii)

• Annual demand = 20,000 filters × 12 = 240,000 filters
• Ordering cost per order = $40
• Carrying cost per unit per annum = $0.05 × 12 = $0.6

Optimal filter order quantity =

=(2 × 240,000 × 40 /0.6)^1/2

= (19,200,000/0.6)^1/2

=(32,000,000)^1/2

= 5,656.85

Since the lot size is 1000, the company will order 6000 filters

The optimal filter order quantity is 6,000 filters

The optimal filter order quantity in lot sizes of 1,000 =

6,000/1,000 = 6

(iii)

• Annual demand = 20,000 filters × 12 = 240,000 filters
• Ordering cost per order = $ 10
• Carrying cost per unit per annum = $0.10 × 12 = $1.2

Optimal filter order quantity =

=(2 × 240,000 × 10 /1.2)^1/2

= (4,800,000/1.2)^1/2

=(4,000,000)^1/2

= 2,000

The optimal filter order quantity is 2,000 filters

The optimal filter order quantity in lot sizes of 1,000 =

2,000/1,000 = 2

Summary:

(i) 4

(ii) 6

(iii) 2