Pocket Park Redesign: Area, Fencing, and Budget Trade-Offs
A neighborhood association is redesigning a rectangular pocket park that measures 36 m by 24 m. The current design places a 2 m wide walking path around the entire inside perimeter, leaving a central garden. A proposed alternative puts a single 3 m wide straight path along one 36 m side and uses the rest for garden, with a circular fountain of radius 4 m at the center of the garden. The association has a budget of $27,500. Paving costs $38 per square meter, garden soil and plants cost $22 per square meter, and the fountain costs $4,800 installed. The city requires that at least 55% of the park's area remain planted garden. A local donor will contribute $2,500 only if the fountain is included. The association also wants a 1.2 m high fence along the outer boundary; fencing costs $46 per linear meter and is sold in 10 m rolls for $440 per roll, with no partial-roll discount. They need to choose a design that stays within budget and meets the garden requirement.
1. For each design, calculate the paved area, planted garden area, and garden percentage. Which designs satisfy the 55% requirement?
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Total park area = 36 × 24 = 864 m². Design 1: the path is an inside ring 2 m wide, so the garden is (36 − 4)(24 − 4) = 32 × 20 = 640 m². Path = 864 − 640 = 224 m². Garden share = 640/864 = 74.1%, above 55%. Design 2: path = 36 × 3 = 108 m²; remaining area = 756 m²; fountain area = π × 4² ≈ 50.27 m²; planted area = 756 − 50.27 = 705.73 m². Garden share = 705.73/864 = 81.7%, also above 55%. Design 2 leaves more planted area despite the wider path because Design 1's ring removes strips from both dimensions.
2. Include the fence cost and the donor contribution. Which design fits the $27,500 budget?
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Fence: perimeter = 2(36 + 24) = 120 m; rolls = 120/10 = 12; cost = 12 × $440 = $5,280. Design 1: paving 224 × $38 = $8,512; planting 640 × $22 = $14,080; fence $5,280; total = $27,872. This exceeds the budget by $372. Design 2: paving 108 × $38 = $4,104; planting 705.73 × $22 = $15,526.06; fountain $4,800; fence $5,280; subtotal = $29,710.06; donor −$2,500 = $27,210.06. Design 2 fits with $289.94 to spare. The donor condition is met because the fountain is included.
3. If the association chooses Design 2, how much can the paving cost per square meter rise before the budget is exceeded? How robust is that margin?
Read the worked answer
Headroom = $27,500 − $27,210.06 = $289.94. Paving area is 108 m². Allowable increase = 289.94/108 ≈ $2.68 per m², so paving could rise to about $40.68/m² before the design exceeds budget. This is a margin of only about 7%, and it assumes the fountain quote and fence roll count stay fixed. The association should obtain firm bids and keep a contingency. If paving rises by more than $2.68/m², Design 2 fails; Design 1 already fails by $372, so neither option is robust without value engineering or a larger donor contribution.