SY Manufacturers (SYM) is producing T-shirts in three colors: red, blue, and white. The monthly demand for each color is 3,000 units. Each shirt requires 0.5 pound of raw cotton that is imported from Luft-Geshfet-Textile (LGT) Company in Brazil. The purchasing price per pound is $2.50 (paid only when the cotton arrives at SYM's facilities) and transportation cost by sea is $0.20 per pound. The traveling time from LGT's facility in Brazil to the SYM facility in the United States is two weeks. The cost of placing a cotton order, by SYM, is $100 and the annual interest rate that SYM is facing is 20 percent.
a. What is the optimal order quantity of cotton?
b. How frequently should the company order cotton?
c. Assuming that the fi rst order is needed on April 1, when should SYM place the order?
d. How many orders will SYM place during the next year?
e. What is the resulting annual holding cost?
f. What is the resulting annual ordering cost?
g. If the annual interest cost is only 5 percent, how will it affect the annual number of orders, the optimal batch size, and the average inventory? (You are not expected to provide a numerical answer to this question. Just describe the direction of the change and explain your answer.)