Raised-Bed Soil Order: Bagged vs. Bulk
A neighborhood greenhouse cooperative is rebuilding three identical raised beds for its spring seedling program. Each bed is rectangular: 2.4 m long, 1.2 m wide, and 30 cm tall. The plan is to leave the soil surface 5 cm below the top edge. The supplier sells bagged potting soil in 40 L bags for $8.50 each. It also delivers bulk soil at $72.00 per cubic metre, but the bulk order has a 0.5 m³ minimum and must be dumped in the parking lot, where volunteers will wheelbarrow it inside. The supplier recommends ordering 8% extra soil to allow for settling and spillage. The cooperative has $600 for soil and limited covered storage: any bagged soil left over must stay dry, while bulk soil cannot be stored on site after the workday. Members disagree about which option is cheaper and whether the bulk minimum matters.
1. Calculate the total volume of soil the cooperative must order, including the 8% settling allowance. Report the result in cubic metres and litres, and show the unit conversions.
Read the worked answer
Effective depth = 30 cm - 5 cm = 25 cm = 0.25 m. One bed: 2.4 m × 1.2 m × 0.25 m = 0.72 m³. Three beds: 3 × 0.72 = 2.16 m³. The 8% allowance is 0.08 × 2.16 = 0.1728 m³. Total = 2.16 + 0.1728 = 2.3328 m³. Since 1 m³ = 1000 L, this is 2.3328 × 1000 = 2332.8 L. Check: 1 L = 0.001 m³, so 2332.8 L × 0.001 = 2.3328 m³, which matches.
2. Compare the cost of bagged soil and bulk soil at the required volume. Include the number of bags that must actually be purchased and the bulk minimum. Which option is cheaper, and by how much?
Read the worked answer
Bagged: 2332.8 L ÷ 40 L per bag = 58.32 bags. Bags cannot be split, so buy 59 bags. Cost = 59 × $8.50 = $501.50. Bulk: the required volume is 2.3328 m³, which is above the 0.5 m³ minimum. Cost = 2.3328 × $72.00 = $167.96, rounded to the nearest cent. Difference = $501.50 - $167.96 = $333.54. Bulk is cheaper by about $333.54 and leaves no bagged soil to store. The 0.5 m³ minimum does not bind because 2.3328 > 0.5.
3. If the cooperative chooses bagged soil, how much soil remains after filling the beds, and how does that leftover affect the decision? Consider both cost and the storage constraint.
Read the worked answer
59 bags contain 59 × 40 = 2360 L. The beds require 2332.8 L, so leftover = 2360 - 2332.8 = 27.2 L, or 27.2 ÷ 1000 = 0.0272 m³. The leftover is small but must be kept dry under the cooperative's storage rule. Cost remains $501.50, still within the $600 budget. The leftover does not erase the bulk savings: bulk costs $167.96 and leaves no material on site, while bagged soil costs $333.54 more and creates a small storage task. Unless volunteers cannot move bulk soil from the parking lot before the workday ends, bulk is the better financial choice. If access is impossible, bagged soil is feasible but uses most of the budget.