Question

SY Manufacturers (SYM) is producing T-shirts in three colors: red, blue, and white. The monthly demand for each color is 3,487 units. Each shirt requires 0.75 pound of raw cotton that is imported from the Luft-Geshfet-Textile (LGT) Company in Brazil. The purchasing price per pound is $1.55 (paid only when the cotton arrives at SYM's facilities) and transportation cost by sea is $0.70 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 $186 and the annual interest rate that SYM is facing is 32 percent of total cost per pound.

a. What is the optimal order quantity of cotton? (Round your answer to the nearest whole number.)
Optimal order quantity pounds
b. How frequently should the company order cotton? (Round your answer to 2 decimal places.)
Company orders once every months
c. Assuming that the first order is needed on 1-Jul, when should SYM place the order?
17-Jun
1-Jul
15-Jul
d. How many orders will SYM place during the next year? (Round your answer to 2 decimal places.)
Number of orders times
e. What is the resulting annual holding cost? (Round your answer to the nearest whole number.)
Annual holding cost $ per year
f. What is the resulting annual ordering cost?
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?

Answer 1

Answer: See explanation

Step-by-step explanation:

a. The optimal order quantity can be calculated as:

= √2DS/H

where

D = 3 × 12 × 3487 × 0. 75

= 94149

Total cost incurred during purchase

= $1.55 + $0.70

= $2.25

Setup cost (S) = $186

Holding cost

= 32% × $2.25

= 0.32 × $2.25

= $0.72

Optimal order quantity

= √(2 × 94149 × 186)/0.72

= 6974.50

b. This will be calculated as:

Annual demand / EOQ

= 94149/6974.50

= 13.50

The company should order cotton 13.5 times per year.

c. Since the first order is needed on 1-July and lead time is 2 weeks, SYM should place the order before 17th June.

d. This will be:

= Annual demand / EOQ

= 94149/6974.50

= 13.5 orders

e. The resulting annual holding cost will be:

= 0.72 × (6974.50/2)

= 0.72 × 3487.25

= $2510.82

f. The resulting annual ordering will be:

= 94149/6974.50 × $186

= 13.5 × $186

= $2511