Gce Model Questions Vol1 2023 Commerce Question 45

A warehouse has a floor area of \(2{,}400\ \text{m}^2\) and a ceiling height of \(6\ \text{m}\), giving a total volume of \(14{,}400\ \text{m}^3\). Three products are stored:\n\n- Product A requires a clearance height of \(2\ \text{m}\) and has a turnover rate of 4 times per year.\n- Product B requires a clearance height of \(3\ \text{m}\) and has a turnover rate of 2 times per year.\n- Product C requires a clearance height of \(4\ \text{m}\) and has a turnover rate of 1 time per year.\n\nThe manager must allocate floor area to each product, with minimum areas of \(600\ \text{m}^2\) for A, \(400\ \text{m}^2\) for B, and \(200\ \text{m}^2\) for C. The total allocated floor area cannot exceed \(2{,}400\ \text{m}^2\) and the total stored volume cannot exceed \(14{,}400\ \text{m}^3\). Assuming the floor area needed for each product equals its stored volume divided by its clearance height, determine the optimal floor‑area allocation (in \(\text{m}^2\)) to products A, B and C that maximises the total annual turnover (turnover rate × stored volume).