To make one bookshelf, a carpenter needs the following things—4 long wooden panels, 8 short wooden panels, 16 small clips, 4 large clips, 32 screws. The carpenter has a stock of 264 long wooden panels, 306 short wooden panels, 2400 small clips, 120 large clips, and 2800 screws. How many bookshelves can the carpenter make? Discuss your thoughts.
Given: 1 bookshelf requires: 4 long panels, 8 short panels, 16 small clips, 4 large clips, 32 screws Stock: 264 long panels, 306 short panels, 2400 small clips, 120 large clips, 2800 screws
Calculation: Long panels: 264 ÷ 4 = 66 bookshelves Short panels: 306 ÷ 8 = 38 bookshelves (remainder 2) Small clips: 2400 ÷ 16 = 150 bookshelves Large clips: 120 ÷ 4 = 30 bookshelves Screws: 2800 ÷ 32 = 87 bookshelves (remainder 16)
Answer: The limiting factor is large clips (minimum value). ∴ The carpenter can make 30 bookshelves.
Explanation
We need to find how many bookshelves can be made from each material: Long panels: 264 ÷ 4 = 66 bookshelves. Short panels: 306 ÷ 8 = 38 bookshelves (remainder 2). Small clips: 2400 ÷ 16 = 150 bookshelves. Large clips: 120 ÷ 4 = 30 bookshelves. Screws: 2800 ÷ 32 = 87 bookshelves (remainder 16). The limiting factor is large clips, which only allows 30 bookshelves.
Solution Steps
Step 1: Long panels: 264 ÷ 4 = 66 bookshelves possible
Step 2: Short panels: 306 ÷ 8 = 38 bookshelves (remainder 2)
Step 3: Small clips: 2400 ÷ 16 = 150 bookshelves
Step 4: Large clips: 120 ÷ 4 = 30 bookshelves
Step 5: Screws: 2800 ÷ 32 = 87 bookshelves (remainder 16)
Step 6: Minimum = 30 bookshelves (limited by large clips)