Jan Kottas is the owner of a small company that buys and resells electric knives used to cut fabric. The annual demand is for 8,000 knives, and Jan is currently buying from Knives-R-Us. The ordering cost is $100 per order. The carrying cost per year is 4% of the acquisition cost of the knife, which is $20.00.

Jan has been approached by Knives-R-Us about buying knives under a new pricing schedule. One option is to order the knives in quantities between 1400 and 1599. If she does this, Knives-R-Us will lower the acquisition price to $19.75 each. If she buys 1600 or more at a time, the company will lower the price to $19.50. Of course, for all other quantities she can still buy the knives at $20.00 per knife.

If your order quantities are in fraction of units, leave them that way.

a) Considering the total cost, composed of the holding cost and ordering cost and including the acquisition cost of the knives, how many should she buy per order to realize the lowest total cost?

b) Provide the lowest total cost for each of the three price options: $19.50, $19.75, and $20.00. Include the holding, ordering and acquisition cost.