Cement storage logistics: A warehouse has internal plan dimensions 15 m × 5.6 m, with a maximum stack (pile) height of 2.70 m. What is the maximum number of cement bags that can be stored in two piles?

Introduction / Context:
Stacking cement requires respecting recommended pile heights and planning the footprint to utilize space safely. Estimating bag capacity from store dimensions is a routine site-planning task for procurement and logistics.

Given Data / Assumptions:

• Internal plan size = 15 m × 5.6 m → area = 84 m^2.
• Maximum pile height = 2.70 m (about 15 bags high at ~0.18 m per bag layer).
• Two piles are to be formed, together utilizing most of the available floor area (ignoring narrow peripheral clearances for this estimate).
• Typical 50 kg bag plan size around 0.7 m × 0.5 m when stacked (≈ 0.35 m^2 per bag per layer).

Concept / Approach:
To estimate total bags: compute bags per layer from floor area and then multiply by number of layers. Packing is not perfect; allow a modest packing factor. The final number should align with practical stacking norms and safety.

Step-by-Step Solution:
Plan area A = 15 * 5.6 = 84 m^2.Area demand per bag per layer a ≈ 0.35 m^2; adopt a packing efficiency ~0.90 → effective area per bag ≈ 0.35 / 0.90 ≈ 0.389 m^2.Bags per layer ≈ 84 / 0.389 ≈ 216.Layers allowable by height ≈ 2.70 / 0.18 ≈ 15 layers.Total bags ≈ 216 * 15 ≈ 3240. Accounting for gangways/clearances and forming exactly two piles reduces capacity modestly → about 3000 bags.

Verification / Alternative check:
Volume method: room volume up to 2.7 m ≈ 84 * 2.7 = 226.8 m^3. Bag volume ≈ 50/1440 ≈ 0.035 m^3. Theoretical max ≈ 226.8 / 0.035 ≈ 6480 bags. After applying practical packing/clearance limits and two defined piles, a value near 3000 is reasonable.

Why Other Options Are Wrong:
1500–2500 bags underestimate capacity for the given area and height.4000 bags overshoots once realistic aisles and two-pile arrangement are considered.

Common Pitfalls:
Ignoring safety clearances and overestimating capacity; exceeding recommended stack height (about 15 bags) which risks cement lumping and instability.

Final Answer:
3000 bags.