We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
a. The optimal order quantity of cotton can be calculated using the Economic Order Quantity (EOQ) formula. EOQ = √((2DS)/H), where D is the annual demand (3000 units per month * 12 months), S is the ordering cost ($100), and H is the annual holding cost (interest rate * unit cost per pound).
In this case, the unit cost per pound is the purchasing price ($2.50) plus the transportation cost ($0.20), which equals $2.70. The annual interest rate is 20% of the total cost per pound, so the annual holding cost is 0.20 * $2.70 = $0.54. Plugging these values into the EOQ formula, we get EOQ = √((2 * 3000 * 12 * 100) / 0.54) = 2200 pounds. Therefore, the optimal order quantity of cotton is 2200 pounds.
b. The company should order cotton every month. Since the monthly demand is 3000 units, and each shirt requires 0.5 pounds of cotton, the monthly demand in pounds is 3000 * 0.5 = 1500 pounds. As the optimal order quantity is 2200 pounds, the company should order cotton once every 2200 / 1500 = 1.47 months, which can be rounded to 1.47 months or approximately 1.47 months.
c. Assuming that the first order is needed on April 1, the company should place the order on March 15th. This is because the traveling time from LGT's facility in Brazil to the SYM facility in the United States is two weeks, and the order should arrive on April 1. Therefore, to ensure timely delivery, the order should be placed on March 15th.
d. The number of orders SYM will place during the next year can be calculated by dividing the total annual demand (3000 units per month * 12 months) by the optimal order quantity (2200 pounds). 3000 * 12 / 2200 = 16.36 orders, which can be rounded to 16.36 or approximately 16 orders.
e. The resulting annual holding cost can be calculated by multiplying the average inventory (half of the optimal order quantity) by the annual holding cost per pound. The average inventory is 2200 / 2 = 1100 pounds. The annual holding cost per pound is $0.54. Therefore, the resulting annual holding cost is 1100 * $0.54 = $594 per year.
f. The resulting annual ordering cost can be calculated by multiplying the number of orders (16) by the ordering cost ($100). Therefore, the resulting annual ordering cost is 16 * $100 = $1600 per year.
g. If the annual interest cost is only 5 percent, it would affect the annual number of orders, the optimal batch size, and the average inventory. A lower annual interest cost means a lower annual holding cost. With a lower holding cost, the optimal batch size may increase, resulting in a decrease in the average inventory. The number of orders would also decrease as the holding cost is lower.
To summarize:
- With a lower holding cost, the batch size may increase.
- A higher batch size would result in a decrease in the average inventory.
- The number of orders would decrease with a lower holding cost.
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