A mail-order house uses 18,000 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are \$96. The following price schedule applies. Determine

Ans:

 Price Level: 1 2 3 4 Minimum quantity for price Qmin = 1000 2000 5000 10000 Price P = 1.25 1.2 1.15 1.1 Optimal Q (for each price) Qopt = 2400 2400 5000 10000 Number of orders per year D/Qopt = 7.5 7.5 3.6 1.8 Average Inventory Qopt/2 = 1200 1200 2500 5000 Annual carrying cost (Qopt/2) * H = 720 720 1500 3000 Annual ordering cost (D/Qopt) * S = 720 720 345.6 172.8 Annual purchase cost P * D = 22500 21600 20700 19800 Total Annual Cost TC = 23940 23040 22545.6 22972.8

Annual Demand

D =

18000

Ordering cost per order

S =

96

Annual carrying cost per unit:

H (fixed) =

0.6

 1

TRUE

H (% of price) =

Optimal Q (overall)

Qopt =

5000

Actual Order Quantity

Q =

Increment

Q =

Price

P =

1.15

Number of orders per year

D/Q =

3.6

Average Inventory

Q/2 =

2500

Annual carrying cost

(Q/2) * H =

1500

Annual ordering cost

(D/Q) * S =

345.6

Annual purchase cost

P * D =

20700

Total Annual Cost

TC =

22545.6

a.The optimal order quantity.

Ans:

Optimal order quantity = 5000

b.The number of orders per year.

Ans: Number of orders per year = 3.6