Worked Solution
✓ VerifiedPreliminary Calculations:
Annual production required = Sales demand − Opening stock of Product X = 5,00,000 − 12,000 = 4,88,000 units
Since A:B = 1:4 (by units) and 4 units of Material A are required per unit of Product X, Material B required per unit = 4 × 4 = 16 units.
Net annual purchases (after adjusting opening raw material stock):
- Material A: (4 × 4,88,000) − 24,000 = 19,52,000 − 24,000 = 19,28,000 units
- Material B: (16 × 4,88,000) − 52,000 = 78,08,000 − 52,000 = 77,56,000 units
Carrying cost per unit p.a.: C_A = 13% × ₹150 = ₹19.50; C_B = 13% × ₹200 = ₹26.00
Ordering cost (O) = ₹15,000 per order
(i) EOQ — Separate Purchase Orders [₹15,000 per material per order]
EOQ = √(2DO/C)
EOQ for A = √(2 × 19,28,000 × 15,000 / 19.50) = √2,96,61,53,846 ≈ 54,465 units
EOQ for B = √(2 × 77,56,000 × 15,000 / 26) = √8,94,92,30,769 ≈ 94,600 units
(ii) EOQ — Combined Purchase Orders [one ₹15,000 ordering cost covers both materials]
When ordered together, A and B must be ordered at the same frequency. The optimal number of combined orders per year:
n = √[(D_A × C_A + D_B × C_B) / (2 × O)]
= √[(3,75,96,000 + 20,16,56,000) / 30,000]
= √[23,92,52,000 / 30,000] = √7,975.07 ≈ 89.3 orders p.a.
EOQ for A (combined) = 19,28,000 ÷ 89.3 ≈ 21,590 units per order
EOQ for B (combined) = 77,56,000 ÷ 89.3 ≈ 86,853 units per order
Note: Under combined ordering, the company places fewer total orders (89.3 vs 35 + 82 = 117 separate orders), saving ordering costs; carrying costs adjust accordingly.
Write it like this
1The skeleton
- Start with a 'Preliminary Calculations' block — derive net production (5,00,000 − 12,000) first, THEN materials; examiners follow this chain and award step marks even if your final EOQ is off.
- Show the ratio-to-units conversion explicitly — write 'Material B per unit of X = 4 (A) × 4 (ratio) = 16 units' as a standalone line; skipping this kills 1–2 marks because the examiner can't see your logic.
- Deduct opening RM stock before plugging D into the formula — net annual purchase is what feeds EOQ, not gross production demand; missing this adjustment is a full-concept error even though everything else is right.
- State the EOQ formula (√2DO/C) before every sub-part — for Part (i) label O = ₹15,000 per material; for Part (ii) label O = ₹15,000 shared; this signals to the examiner you know WHY the two parts differ.
- For combined orders, show the n-formula working numerically — write out (D_A × C_A + D_B × C_B) in the numerator explicitly; then divide each annual demand by n to get per-order quantities; examiners reward the method, not just the final number.
- Close Part (ii) with a one-line comparative note — '89.3 combined orders vs 117 separate orders, hence lower ordering cost' — this shows understanding and picks up the 'analysis' mark many students leave on the table.
2Examiner-rewarded phrases
3Common trap
Most students forget to subtract opening Product-X stock before computing raw material demand — they directly use 5,00,000 units and get wrong D values throughout. Also watch out for Part (ii): a huge chunk of students apply ₹15,000 separately to each material even in the combined-order scenario, which defeats the entire point of the question and makes your answer identical to Part (i).