KC Engineering Works (KCEW) sells compressors for air conditioning units to several HVAC dealers in the Midwest region. The annual demand for the compressors is 65,000 units. For the reasons of simplicity assume that the demand is uniform throughout the year. Each compressor unit weighs 10 lbs. KCEW buys the compressors at $130 a piece directly from the manufacturer based in Louisville, KY, in batch sizes that minimize its overall cost. They maintain a safety stock that is 25% of the demand during the lead-time and that the holding cost is 18% of the cost per compressor per year. They have received the following transportation proposals from different providers. Assume 260 days per year. (1 cwt = 100 lbs)

Carrier Name	Minimum Shipment (cwt)	Rate ($/cwt)	Lead Time (days)
BNSF Railway	300+	8.50	12
C.H. Robinson	50+	14.00	8
UPS Supply Chain Solutions	100-200	12.00	9
	200-400	8.50	9
	400+	6.50	9

a) What is KCEWs annual holding cost for pipeline stock if KCEW uses C.H. Robinson as the transportation provider?

b) What is the average safety stock at KCEW (in units of product) if KCEW uses BNSF Railway as the transportation provider?

c) Ignoring the annual purchasing cost of the compressors (which is $13065,000 = $8.45M), what is the total annual cost of KCEW if it buys compressors in batch sizes of 2,600 units (i.e., follows a fixed order quantity inventory policy) and uses UPS Supply Chain Solutions as the transportation provider?

d) Should KCEW increase its batch size to 4,000 units from 2,600 units while following a fixed order policy and using UPS Supply Chain Solutions as the transportation provider? Justify your answer numerically.