Two Binding Quotes with a Hidden Minimum
A two-person print co-op has won a contract for 1,850 copies of a 240-page community history booklet. Two binding quotes are on the table. Supplier A charges a 145-unit setup fee plus 2.35 units per copy, with no minimum. Supplier B charges 420 units setup plus 1.90 units per copy, but its line will not start below 2,000 copies, so the co-op would receive, and pay for, 2,000 units, discarding 150. Both quotes exclude an 8% sales tax, and either supplier adds a flat 60-unit delivery charge after tax. The co-op's treasurer has budgeted 5,200 units in total and wants to know which quote to accept. A volunteer has already argued that B is cheaper 'because the per-copy price is lower and the run is nearly 2,000 anyway.' The co-op also expects a second, similar contract next year and is unsure of its size.
1. Calculate the total cost of each quote, including tax and delivery. State which is cheaper for this order and by how much, and whether either exceeds the budget.
Read the worked answer
Work through each quote in the same order: copies, setup, tax, delivery.
Supplier A
- Copies: 1,850 × 2.35 = 4,347.50
- Add setup: 4,347.50 + 145 = 4,492.50
- Tax at 8%: 4,492.50 × 0.08 = 359.40, giving 4,851.90
- Add delivery: 4,851.90 + 60 = 4,911.90
Supplier B
- Payable copies: 2,000 (the minimum), so 2,000 × 1.90 = 3,800
- Add setup: 3,800 + 420 = 4,220
- Tax at 8%: 4,220 × 0.08 = 337.60, giving 4,557.60
- Add delivery: 4,557.60 + 60 = 4,617.60
B is cheaper by 4,911.90 − 4,617.60 = 294.30 units. Both totals sit below the 5,200-unit budget, so the budget does not decide the question. Note that the saving is only about 6% of the order value, which matters when weighing risk.
2. At what order size would the two quotes cost the same, taking B's 2,000-copy minimum into account? Explain what happens either side of that size.
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Because tax is a percentage of the subtotal and delivery is a flat charge added to both, the break-even quantity is the same before and after tax and delivery. Compare pre-tax subtotals.
For any order at or below 2,000 copies, B still charges for 2,000, so B's subtotal is fixed: 420 + (2,000 × 1.90) = 4,220.
A's subtotal is 145 + 2.35q.
Set them equal: 145 + 2.35q = 4,220 2.35q = 4,075 q = 1,734.04
So at about 1,734 copies the two are level (A: 145 + 2.35 × 1,734.04 = 4,220). Below that, A is cheaper; above it, B is cheaper even though B charges for 2,000 copies. At 1,850, B wins, which matches the first task.
If the order were above 2,000, B's minimum no longer binds and B's subtotal becomes 420 + 1.90q. Setting 145 + 2.35q equal to that gives q = 611, so beyond 2,000 B is always the cheaper option. The interesting threshold is therefore the 1,734 figure, not 2,000.
3. Assess the volunteer's reasoning. What should the co-op decide for this order, and what should it do about next year's contract?
Read the worked answer
The volunteer reaches the right conclusion for the wrong reason. A lower per-copy price does not by itself make a quote cheaper: B's higher setup fee and, more importantly, its 2,000-copy minimum both raise the total. The correct comparison is total cost at the actual quantity, which is what the first task computes. The phrase 'nearly 2,000 anyway' also hides the fact that 150 books are paid for and discarded, so the co-op is buying 8% more product than it needs.
For this order, accept B: the 294.30 saving is real and both quotes fit the budget. But the margin is thin relative to the order, and it depends entirely on volume. If next year's contract falls below roughly 1,734 copies, A becomes cheaper, and below 2,000 B's minimum forces payment for unwanted stock.
Practical steps: (1) take B for the current run; (2) before committing next year, get a realistic quantity forecast, since the 1,734 threshold is the decision line; (3) ask whether the 150 surplus copies could be sold or given to contributors, which would recover some value; (4) ask B whether the minimum is negotiable, since removing it would change the comparison entirely.