Question

Betty bakes and sells bagels all year round. Betty plans and manages inventories of paper take-out bags with her logo printed on them. Daily demand for take-out bags is normally distributed with a mean of 90 bags and a standard deviation of 30 bags. Betty’s printer charges her $10 per order for print setup independent of order size. Bags are printed at 5 cents ($0.05) each bag. It takes 4 days for an order to be printed and delivered. Betty has a storage room big enough to hold all reasonable quantities of bags. The holding cost is estimated to be 25% per year. Assume 360 days per year. (Use the H= i × C formula to compute the annual holding cost). Please solve H and I.  Please show work. Thanks.

H. If Betty’s printer charges her $12 per order irrespective of order size, what is the total annual inventory-related costs per bag?

I. Assume that the print cost can be reduced to 3 cents per bag if Betty prints 9000 bags or more at a time. If Betty is interested in minimizing her total cost (i.e., purchase and inventory-related costs), should she begin printing 9000 or more bags at a time?

Answer 1

Given,

Annual demand = D = d x number of days in a year = 90 x 360 = 32400 bags

Order cost = $12

Cost of bag = $0.05

Holding Cost = H = 25% of 0.05 = $0.0125

EOQ = = = 7887.2 bags

Total inventory cost = Total Ordering cost + Total Holding cost

Total inventory cost = =

Total Inventory cost = 49.3 + 49.3 = $98.6

I.

For EOQ,

The total cost per bag = The total annual inventory-related costs per bag + Purchase Cost = 98.6 + D * C = 98.6 + 32400 * 0.05 = $1,718.6

For new condition,

Given, Discount = Pd = $0.03

Holding cost = H = 25% * 0.03 = $0.0075

New order quantity,Q = 9000

Total Cost = Annual Ordering Cost + Annual Holding Cost + Purchase Cost

=

=

= 43.2 + 337.5 + 972

= $1,352.7

Total Cost for New Order Quantity,Q = 9000 is less than EOQ (1352.7 < 1718.6)

, hence, She should begin printing 9000 bags at a time.