The Novel Order: A Cost Comparison Under Two Constraints
Ms. Okafor has $450 in classroom funds and needs 26 copies of a novel. The district warehouse sells the title only in packs of 10 for $118.00 per pack; warehouse orders carry 7% sales tax and a flat $15.00 shipping fee. A local bookstore sells single copies at $12.95 each, and purchases through the school's tax-exempt vendor account pay no tax and no shipping. Ms. Okafor must reserve $60 from the same $450 for a science lab kit, and she may not exceed the total. Her principal prefers warehouse orders "when they are cost-effective" but has approved bookstore purchases before.
1. Compute the full cost of filling the order through the warehouse, including the lab kit, and determine whether it fits the budget.
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Step 1 - packs needed. 26 copies ÷ 10 per pack = 2.6, so round up to 3 packs (30 copies). Two packs would leave her 6 copies short.
Step 2 - merchandise: 3 × $118.00 = $354.00
Step 3 - tax: $354.00 × 0.07 = $24.78 (tax applies to merchandise; the problem gives no indication it applies to shipping, and applying it there would change the total by only $1.05, which does not affect the conclusion)
Step 4 - shipping: $15.00
Step 5 - order total: 354.00 + 24.78 + 15.00 = $393.78
Step 6 - add the reserved kit: 393.78 + 60.00 = $453.78
Verdict: over budget by $3.78. The warehouse route fails the constraint, and not by a rounding error - it fails even before any price change.
2. Compute the bookstore cost and make a recommendation. Does the principal's "cost-effective" condition settle the choice?
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Bookstore: 26 × $12.95 = $336.70, no tax, no shipping. With the kit: 336.70 + 60.00 = $396.70, leaving $53.30 unspent.
Comparison: bookstore is cheaper by 393.78 − 336.70 = $57.08 on the books alone, and it is the only option that stays under $450 (by $53.30 versus a $3.78 overage).
Recommendation: buy from the bookstore.
On the principal's condition: the warehouse is not cost-effective here, so the condition points to the bookstore rather than away from it. The usual assumption - bulk packs are cheaper - fails because the pack size (10) does not divide the need (26): she pays for 30 and still pays tax and shipping. Note also that the overage is small, so the honest framing to the principal is "$3.78 over," not "far over." A defensible alternative is to ask whether the warehouse fee can be waived, since that single waiver would flip the total to $378.78.
3. Suppose the $60 lab kit were funded from a different account. Does the recommendation change? What does this reveal about how the constraint was doing the work?
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New comparison, books only:
- Warehouse: $393.78 (fits under $450, with $56.22 left)
- Bookstore: $336.70 (with $113.30 left)
The recommendation does not change. The bookstore is still cheaper by $57.08. Removing the kit constraint makes the warehouse affordable, but affordability and cost-effectiveness are different tests, and the principal asked for the second one.
What this shows: the budget cap eliminated the warehouse option outright, but cost was already eliminating it. Two independent reasons point the same way, which is why the answer is stable - a good check on any word problem whose conclusion depends on a single tight inequality.
The honest trade-off: for $57.08 more, the warehouse delivers 30 copies instead of 26 (4 spares for a classroom library) and keeps spending in the district system. That is a legitimate reason to choose it, but it must be argued as a value judgment, not presented as the cheaper option.