Expert: Josh - 8/22/2009

Question
How many 1 and 3/4 inch long machine bolt blanks can be cut from a 5-foot length of stock? allow 7/32 inch for waste on each blank. I came up with 27 and 17/112.

Answer
Hi Rico,

If we cut N pieces, and each bolt is X in length, the useful portion will be N*X in total length. Because there are (N-1) gaps, (N-1)*(7/32) inches will be wasted.

These two measurements must add up to less than or equal to 5 ft (60 inches). We cannot exceed the amount of material given.

Fact: length of bolt X=7/4 (one and three quarter inches). For convenience, we write this as (7/4)*(8/8)=56/32 inch.

So, we need to find the largest integer N, which satisfies the condition:

N*(56/32)+(N-1)*(7/32) <= 60

Simplifying,
N*[(56/32)+(7/32)] - 7/32 <= 60
N*[(56/32)+(7/32)] <= 60 +(7/32)
N <= [60 +(7/32)]/[(56/32)+(7/32)]
N <= 30.5873...

I think the maximum number N is 30.

Please check that I haven't made any silly mistake as my blood sugar level is pretty low at the moment ;)