Star Toys Company produces dolls using flesh colored cloth in its doll production process. Annual requirements of flesh colored cloth are 2,500,000 square yards for smooth production and sales of…

a. Economic Order Quantity (EOQ)

The EOQ formula is derived by minimizing total inventory costs (ordering + holding):

$$EOQ=\sqrt{\frac{2DS}{H}}$$

Given:

• Annual demand ($D$) = 2,500,000 sq. yds.
• Ordering cost ($S$) = Rs 4,000 (fixed cost per order)
• Holding cost ($H$) = 20% of Rs 1,000 = Rs 200 per sq. yd. per year

Calculation: $$EOQ=\sqrt{\frac{2\times 2,500,000\times 4,000}{200}}=\sqrt{100,000,000}=\text{10,000 sq. yds.}$$

---

b. Total Cost of Inventory

Total inventory cost = Ordering cost + Holding cost

1. Ordering Cost = $\frac{D}{Q}\times S=\frac{2,500,000}{10,000}\times 4,000=100\times 4,000=\text{Rs 400,000}$
2. Holding Cost = $\frac{Q}{2}\times H+SS\times H=\frac{10,000}{2}\times 200+15,000\times 200=1,000,000+3,000,000=\text{Rs 4,000,000}$

Total Inventory Cost = Rs 400,000 + Rs 4,000,000 = Rs 4,400,000

---

c. Re-order Point (ROP)

The ROP ensures that safety stock is maintained during lead time:

$$ROP=\text{Average Daily Usage}\times \text{Lead Time}+\text{Safety Stock}$$

Given:

• Lead time = 2 weeks = 10 working days (assuming 5-day workweek)
• Annual demand = 2,500,000 sq. yds. → Daily demand = $\frac{2,500,000}{300}\approx 8,333.33$ sq. yds.

Calculation: $$ROP=8,333.33\times 10+15,000=83,333.33+15,000=\text{98,333 sq. yds.}$$