Practise the method.
Example 1
A club needs at least 28 notebooks. Small boxes hold 4 and cost $10; large boxes hold 8 and cost $12. At most 3 large boxes are available; small boxes are unlimited. Delivery costs $2 per box, in addition to its price. Boxes cannot be split. What is the least total cost in dollars?
Show worked answer
Answer: 54
- Include delivery in both box prices.
- For each possible large-box count from 0 to 3, round up the small boxes needed.
- The minimum is 3 large and 1 small boxes, costing $54.
Example 2
A delivery has 6 standard boxes and 4 large boxes, with 130 items altogether. Large boxes each hold 5 more items than standard boxes. Discard 3 damaged standard boxes and keep 7 further items as samples. Repack the rest into 3−item packs and 5−item packs, making exactly 1 more small packs than large packs. Leftover items are allowed. What is the greatest possible number of large packs?
Show worked answer
Answer: 10
- A standard box holds 6+4130−4×5=11.
- That leaves 90 usable items.
- If L large packs are made, small packs number L+1
- 3(L+1)+5L≤90.
- The largest whole-number L is 10.
Example 3
A club needs at least 57 notebooks. Small boxes hold 8 and cost $14; large boxes hold 12 and cost $14. At most 4 large boxes are available; small boxes are unlimited. Delivery costs $6 per box, in addition to its price. Boxes cannot be split. What is the least total cost in dollars?
Show worked answer
Answer: 120
- Include delivery in both box prices.
- For each possible large-box count from 0 to 4, round up the small boxes needed.
- The minimum is 3 large and 3 small boxes, costing $120.