County Hospital orders syringes from a hospital supply firm. The hospital expects to use 40,000 syringes per year. The ordering cost (cost to order and have the syringes delivered) is $800 per order. The annual holding cost per syringe is 20% of the cost of a syringe. The hospital supply firm offers the following quantity discount pricing schedule. Order Quantity Price per Syringe 0 5,999 $3.40 6,000 - 10,999 $3.30 11,000 19,999 $3.26 20,000 and over $3.23.
a) What is the optimal quantity per order based on the total annual cost (composed of the holding cost and ordering cost and the acquisition cost)? Provide the lowest total cost for each of the price options. Include the holding, ordering and acquisition cost.
b) For an exclusive agreement, the supplier has offered to reduce the cost to $3.10 per syringe with no restriction on the order quantity. The ordering cost per order remains the same. If County Hospital selects this option, it will need to increase the annual holding cost per syringe to 23% of the cost of a syringe. Based on the total annual cost, should Douglas County select this option compared to the one found in a)? Explain your answer.