Math CentralQuandaries & Queries


Question from JB:

We buy product in rolls: 54" x 150'. We make a product that is 2 x 3.5 inches out of this roll and sell by the each. How do we convert this? What is the formula to determine how many devices fit in a sq foot. Then we / by 12? PLEASE help. Thank You.


Manufacturing isn't my area of expertise, but I will give this a try. Your final product is 2 x 3.5. Is any of the material lost in the cutting process? If the answer is yes, then it will be necessary to re-do this calculation to include that.

If there is no lost material in the cut, then from each square foot you can get 6 rows of 3 rectangles of size 2 x 3.5. That's 18 units of product per square foot with a loss of 1.5 inches by 12 inches from each square foot used (so the waste is 18 square inches from each 144 square inches (square foot)).

There is a better way than taking the material one square foot at a time if your equipment can handle it. Across 54 inches you can get 27 two inch widths. Along 150 feet = 150x12 inches = 1800 inches you can get 514.29 3.5 inch lengths. Therefore, assuming you cut in a regular grid, the maximum number possible of rectangles you can cut out of your stock is 27 x 514 = 13,878. The maximum number that can be obtained by using the material 54 inches by one foot at a time is 12,150. If you use one square foot at a time, so that 6 inches x 150 feet is wasted, then the maximum is 10,800.

If you can handle strips of material 54 inches wide and 42 inches long, then by cutting as described above you can get 13,608 units of product. If it is possible to also cut the roll end (54 inches by 36 inches), then
you can get the remaining 270 units to make up the absolute maximum obtainable using this method.

I hope this helps.


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