The Makerspace Allocation
The library at Westfield School has a makerspace budget of 1,200 USD for the new term. The librarian must buy at least eight items in total and must include at least one 3D printer, one coding kit, and one safety set. Prices are: 3D printer 450 USD; coding kit 180 USD; safety set 120 USD; filament spool 30 USD; robotics add-on 220 USD; teacher workshop 300 USD. School rules say no more than 50% of the budget may go to any single category, where categories are 'machines' (printer, robotics add-on), 'consumables' (filament), 'training' (workshop), and 'kits/safety' (coding kit, safety set). The librarian wants at least two coding kits and at least three filament spools. A teacher proposes: one printer, two coding kits, one safety set, three filament spools, one robotics add-on, and one workshop. The librarian says this proposal breaks at least one rule. Check it, then propose a revised purchase that meets all rules and costs no more than 1,200 USD.
1. Check the teacher's proposal against the budget and category cap. Show the arithmetic and state every rule it breaks.
Read the worked answer
Total: 450 + (2 × 180) + 120 + (3 × 30) + 220 + 300 = 450 + 360 + 120 + 90 + 220 + 300 = 1,540 USD, which is 340 USD over the 1,200 budget. Category totals: machines = printer 450 + robotics add-on 220 = 670, above the 600 cap; kits/safety = 360 + 120 = 480, within cap; consumables = 90, within cap; training = 300, within cap. The proposal does meet the item-count and minimum-item rules: 9 items, with one printer, two coding kits, one safety set, and three filament spools. So it breaks the total-budget rule and the machines category cap.
2. Propose one purchase plan that satisfies all rules. List items, total cost, and category totals.
Read the worked answer
One valid plan is: one 3D printer (450), two coding kits (360), one safety set (120), and four filament spools (120). Total = 450 + 360 + 120 + 120 = 1,050 USD. Item count = 1 + 2 + 1 + 4 = 8, so the minimum is met. Required items are present, and there are at least two coding kits and three filament spools. Category totals: machines 450 (≤600), kits/safety 480 (≤600), consumables 120 (≤600), training 0. The plan leaves 150 USD unspent, which is allowed because the rules set a maximum, not an exact spend.
3. The librarian wants to add the teacher workshop if possible. Determine whether any valid plan can include the workshop and still meet all rules. Explain.
Read the worked answer
No valid plan can include the 300 USD workshop. Before any workshop, the mandatory minimum is one printer (450), two coding kits (360), one safety set (120), and three filament spools (90): 450 + 360 + 120 + 90 = 1,020 USD. The eight-item rule then requires at least one more item; the cheapest is another filament spool at 30, making 1,050 USD. Adding the workshop would bring the total to 1,350 USD, already over 1,200. Could the librarian drop a required item? No: the printer, one coding kit, and one safety set are mandatory, and the librarian's own rules require two coding kits and three filament spools. So the minimum non-training spend with eight items is 1,050, leaving only 150, less than the 300 workshop. The workshop is therefore impossible under all stated rules.