Gce Model Questions Vol1 2024 Commerce Question 3

A warehouse stocks a product whose daily demand is normally distributed with mean \(120\) units and standard deviation \(30\) units. The company can choose between two lead‑time options: - **Option A**: Lead time \(L=5\) days, no extra cost. - **Option B**: Lead time \(L=3\) days, but an additional cost of \(\£200\) is incurred for each order placed. Holding cost is \(\£0.25\) per unit per day. The profit per unit sold is \(\£0.25\) per unit (i.e., the contribution margin). The company uses a continuous‑review system and orders a fixed quantity \(Q\) each cycle, equal to the expected demand over the lead time. It wishes to maintain a 95 % service level (i.e., the probability of no stock‑out during lead time). Determine which lead‑time option minimises the total expected monthly cost (30 days) and give the corresponding order quantity \(Q\). Show all calculations.