Question

SY manufacturer (SYM) is producing T-shirt in three colors: blue, red, and white. The monthly demand for each color is 3000 units. Each shirt requires 0.5 pound of raw cotton that is imported from LuftGeshfet-Textile (LGT) Company in Brazil. The purchasing price per pound is $2.5 (paid only when the cotton arrives at SYM’s facilities) and transportation cost by sea is $o.2 per pound. The traveling time from LGT’s facilty in Brazil to SYM facility in the United States is two weeks. The cost of placing a cotton order, by SYM, is $100 and the annual interst 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. What is the resulting annual holding cost? d. What is the resulting annual ordering cost?

Answer 1

a) Optimal order Quantity =4,472.13 pounds

b) No of times order per year= 12 times in a years i.e once in a month

c) Annual Holding cost = $1207.47

d) Ordering cost per annum = $1207.47

Step-by-step explanation:

Total annual demand = 3000 ×3 × 12 × 0.5 pounds= 54,000 pounds

Ordering cost per order = 100

Holding cost per order = 20%× (2.5+0.2) = 0.54

Optimal order Quantity = √(2× 100×54000)/0.54

=4,472.13 pounds

No of times order per year

= 54,000/4472.13 = 12 times in a years

that is, once per month.

Annual Holding cost

= Holding cost per unit annum × Average inventory

= 0.54 × 1/2 × 4,472.135 = $1207.47

Ordering cost per annum

=Annual demand/order quantity × ordering cost per order

= 54,000/4472.13 × 100 = $1207.47