The following inventory data have been established for the Cotton Tops Inc. (1) Annual sales are 100,000 units. (2) The purchase price per unit is $2.00 (3) Carrying cost is 3% percent. (4) Cost per order placed is $10. (5) Desired safety stock is 30 days supply. Use this data to compute: (a) EOQ - 3 pts (b) Average Inventory - 2 pts (c) Maximum Inventory - 1 pt (d) Optimal number of orders per year - 1 pts (e) Total inventory cost - 3 pts

a) in order to calculate the EOQ we do not consider safety stock since that is one time purchase.

EOQ = √(2SD / H)

S = order cost = $10

D = annual demand = 100,000 units

H = annual holding cost = $2 x 3% = $0.06

EOQ = √[(2 x $10 x 100,000) / $0.06] = √33,333.33 = 5,773.5 ≈ 5,774

b) average inventory = (5,774 / 2) + (100,000/12) = 2,887 + 8,333 = 11,220 units

c) maximum inventory = 8,333 + 5,774 = 14,107

d) optimal number of orders = 100,000 / 5,774 = 17.32 times

e) total inventory cost = (17.32 x $10) + (11,220 x $0.06) + (100,000 x $2) + (8,333 x $2) = $173.20 + $673.20 + $200,000 + $16,666 = $217,512.40