1. **Problem statement:** Company X uses 4 units daily, 360 days/year. Ordering cost is 10 per order, carrying cost is 2 per unit. Current order size is 144 units. We need to find: a. Total cost for current order size b. EOQ and total cost at EOQ c. Reorder point (ROP) with 5 days lead time d. Safety stock and new ROP if daily usage increases to 6 units 2. **Formulas and rules:** - Total cost (TC) = Ordering cost + Carrying cost + Purchase cost (purchase cost ignored here as not given) - Ordering cost = (D/Q) * S where D = demand, Q = order quantity, S = ordering cost - Carrying cost = (Q/2) * H where H = carrying cost per unit - EOQ = $$\sqrt{\frac{2DS}{H}}$$ - Reorder point (ROP) = daily usage * lead time - Safety stock = (rush daily usage - normal daily usage) * lead time 3. **Given values:** - D = 4 units/day * 360 days = 1440 units/year - S = 10 - H = 2 - Q = 144 units (current order size) - Lead time = 5 days --- **a. Total cost in recent condition:** Ordering cost = $$\frac{D}{Q} \times S = \frac{1440}{144} \times 10 = 10 \times 10 = 100$$ Carrying cost = $$\frac{Q}{2} \times H = \frac{144}{2} \times 2 = 72 \times 2 = 144$$ Total cost = Ordering cost + Carrying cost = $$100 + 144 = 244$$ --- **b. EOQ and total cost at EOQ:** Calculate EOQ: $$EOQ = \sqrt{\frac{2DS}{H}} = \sqrt{\frac{2 \times 1440 \times 10}{2}} = \sqrt{14400} = 120$$ Ordering cost at EOQ: $$\frac{1440}{120} \times 10 = 12 \times 10 = 120$$ Carrying cost at EOQ: $$\frac{120}{2} \times 2 = 60 \times 2 = 120$$ Total cost at EOQ = $$120 + 120 = 240$$ --- **c. Reorder point (ROP) with 5 days lead time:** $$ROP = \text{daily usage} \times \text{lead time} = 4 \times 5 = 20$$ units --- **d. Safety stock and new ROP if daily usage is 6 units:** Safety stock = $$(6 - 4) \times 5 = 2 \times 5 = 10$$ units New ROP = normal ROP + safety stock = $$20 + 10 = 30$$ units --- **Final answers:** a. Total cost current = 244 b. EOQ = 120 units, total cost EOQ = 240 c. ROP = 20 units d. Safety stock = 10 units, new ROP = 30 units