1. **Problem Statement:** John Equipment Company estimates carrying cost at 15% and ordering cost at 9 per order. Annual requirement is 48,000 units at 4 per unit. Find: i) Most economical number of units to order (EOQ). ii) Number of orders to place in a year. 2. **Formula for EOQ:** $$EOQ = \sqrt{\frac{2DS}{H}}$$ Where: - $D$ = Annual demand = 48000 units - $S$ = Ordering cost per order = 9 - $H$ = Holding cost per unit per year = Carrying cost rate \times Unit cost = 0.15 \times 4 = 0.6 3. **Calculate EOQ:** $$EOQ = \sqrt{\frac{2 \times 48000 \times 9}{0.6}} = \sqrt{\frac{864000}{0.6}} = \sqrt{1440000} = 1200 \text{ units}$$ 4. **Calculate number of orders per year:** $$\text{Number of orders} = \frac{D}{EOQ} = \frac{48000}{1200} = 40 \text{ orders}$$ **Final answers:** - Most economical order quantity (EOQ) = 1200 units - Number of orders per year = 40 orders