Juice stock: choosing a supplier when the crate sizes do not match the order
Marcia sells bottled juice at the gate of a primary school in Region 4. She needs 288 bottles for the two-week term opening and has two suppliers. Supplier A sells crates of 24 bottles at $2,760 per crate and charges a flat $450 delivery fee per order. Supplier B sells crates of 20 bottles at $2,400 per crate, delivers free, and takes 5% off the crate price when an order is 15 crates or more. Crates cannot be split. Marcia plans to sell every bottle at $200. She has no cool storage, so bottles left over after the opening week are usually wasted. A parent suggests a '3 bottles for $500' deal to speed up sales, arguing that 'cheaper means more customers, so more money'.
1. Work out the total cost of at least 288 bottles from each supplier. Show the crate counts and the effect of the 5% discount.
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Supplier A
- 288 ÷ 24 = 12 exactly, so 12 crates, giving exactly 288 bottles.
- 12 × $2,760 = $33,120
- Plus delivery: $33,120 + $450 = $33,570
- Cost per bottle: $33,570 ÷ 288 ≈ $116.56
Supplier B
- 288 ÷ 20 = 14.4, and crates cannot be split, so 15 crates = 300 bottles.
- 15 × $2,400 = $36,000
- Discount applies because 15 crates meets the threshold: 5% of $36,000 = $1,800
- $36,000 − $1,800 = $34,200, delivery free
- Cost per bottle: $34,200 ÷ 300 = $114.00
Supplier B is $630 dearer in total but supplies 12 extra bottles. Supplier A's crate size fits the order exactly; B's lower price per bottle only pays off if those 12 bottles are actually sold.
2. Marcia is sure she can sell 288 bottles but cannot sell leftovers. Which supplier gives the greater profit, and how many of the extra bottles would she need to sell to change that answer?
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Sales: 288 × $200 = $57,600
- Supplier A profit: $57,600 − $33,570 = $24,030
- Supplier B profit: $57,600 − $34,200 = $23,400
Supplier A is ahead by $630, because B's 12 extra bottles are paid for but thrown away.
When does B win? Each extra bottle sold brings $200. B starts $630 behind, so she needs extra sales worth more than $630:
- 3 bottles = $600 - still behind
- 4 bottles = $800 - now ahead
So selling just 4 of the 12 surplus bottles (at least 3.15, rounded up to 4) makes Supplier B the better choice. If she sells all 12: B profit = $60,000 − $34,200 = $25,800, $1,770 more than A.
The decision turns on a forecast, not on the invoice: if she can move the surplus quickly, B wins; if not, A's exact fit is safer.
3. Test the parent's claim that '3 bottles for $500' will bring in more money. Use a batch of 60 bottles sold under the deal as your example.
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Price per bottle under the deal: $500 ÷ 3 ≈ $166.67, against $200 at the single price - she gives up about $33.33 on every bottle sold this way.
60 bottles sold as 3-for-$500:
- 60 ÷ 3 = 20 deals; 20 × $500 = $10,000
- At the single price: 60 × $200 = $12,000
- Loss = $2,000
The parent's claim confuses more customers with more money. A lower price adds money only if it sells bottles that would otherwise stay unsold. Marcia's stock is fixed at 288 and she already expects to sell all of them, so the deal cannot create extra sales - it only cuts the price on bottles she would have sold anyway.
What would be needed: to recover $2,000 at $166.67 per bottle she would need 12 additional bottles sold (12 × $166.67 ≈ $2,000). That means buying roughly one more crate, which contradicts her no-storage constraint. Recommendation: keep the $200 price, or run the deal only on stock she would otherwise waste.