Two maize-meal quotations for the hostel term
Kandjimi runs the tuck shop at a combined school and has to order 400 bags of maize meal for the hostel term. Two wholesalers submitted written quotations, and both state that prices exclude 15% VAT.
Wholesaler A: N$42.50 per 12.5 kg bag, with an 8% discount on the order value (before delivery) if that value exceeds N$12 000, plus a fixed delivery charge of N$180.
Wholesaler B: N$44.00 per 12.5 kg bag, free delivery, and a promotion of 'pay for 10, get 1 free' on identical bags.
The hostel committee also wants the bags resold to staff at a price that gives at least 25% profit on the landed cost per bag, rounded to the nearest 50 cents. In the second term enrolments drop and Kandjimi expects to need only 250 bags. A committee member argues that Wholesaler B is obviously cheaper because the free bags are effectively a discount.
1. Calculate the landed cost, including VAT, of 400 bags from each wholesaler and state which quotation is cheaper.
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Wholesaler A
Order value before discount = 400 × 42.50 = N$17 000. This exceeds N$12 000, so the 8% discount applies: 0.08 × 17 000 = N$1 360, leaving 17 000 − 1 360 = N$15 640. Add delivery: 15 640 + 180 = N$15 820 excluding VAT. Including VAT: 15 820 × 1.15 = N$18 193.00.
Wholesaler B
Bags arrive in groups of 11, of which 10 are paid for. 400 ÷ 11 = 36 groups with 4 bags left over (36 × 11 = 396). Paid bags = 36 × 10 + 4 = 364. Cost = 364 × 44.00 = N$16 016 excluding VAT; × 1.15 = N$18 418.40.
Conclusion: A is cheaper by N$225.40 including VAT.
The threshold is the judgement point: at 400 bags A's order value of N$17 000 crosses N$12 000, so the discount is earned. Note also that B's promotion gives the larger reduction per bag (N$4.00 off N$44.00, i.e. 9.1%) than A's 8% (N$3.40 off N$42.50), but B's list price is N$1.50 higher, so A still wins.
2. Find the selling price per bag, rounded to the nearest 50 cents, that gives at least 25% profit on the landed cost, and verify that the price chosen satisfies the requirement.
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Landed cost per bag = 18 193.00 ÷ 400 = N$45.4825.
Price at exactly 25% profit = 45.4825 × 1.25 = N$56.853.
Rounding to the nearest 50 cents gives N$57.00, because N$56.50 would give 56.50 ÷ 45.4825 = 1.2423, i.e. only 24.2% profit, which fails the requirement. The direction of rounding is fixed by the constraint, not by the usual convention.
Check: 57.00 ÷ 45.4825 = 1.2532, so profit is 25.3% ≥ 25%. If all 400 bags sell, income = 400 × 57.00 = N$22 800 and profit = 22 800 − 18 193 = N$4 607.
Judgement: 'nearest 50 cents' and 'at least 25%' can pull in opposite directions; the answer must satisfy the constraint, so rounding up is correct here.
3. Recalculate both quotations for an order of 250 bags and comment on the committee member's claim that Wholesaler B is obviously cheaper because of the free bags.
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Both prices exclude VAT, so a common 15% factor leaves the ranking unchanged; work without VAT and state that assumption.
A: 250 × 42.50 = N$10 625, which is below the N$12 000 threshold, so no discount is earned: 10 625 + 180 = N$10 805.
B: 250 = 22 × 11 + 8, so paid bags = 22 × 10 + 8 = 228 and cost = 228 × 44 = N$10 032.
B is cheaper by N$773.
Judgement on the claim: the member is right at 250 bags but wrong at 400 bags. The free-bag promotion works on every order, whereas A's 8% discount is conditional on order size. Reducing the order therefore flips the decision: A's effective price per bag rises from N$39.55 to N$43.22, while B's falls only slightly. The correct procedure is to cost each order size separately and to identify the threshold as the deciding factor, not to assume a fixed preference between suppliers.