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# 'Optimal circle packing' questions watch

1. (A) At present a disk-pressing machine is set to cut out 16 disks, each of diameter 0.25m, from a 1 square metre aluminium sheet. There is also a further need to cut disks, each of diameter 0.1m, from the same sheets. The firm needs twice the number of small disks as they do large disks. What is the best arrangement of cutting heads to minimise wastage?

(B) As an extension, and more generally, the manager wants to invest in a continuous strip processing machine, that will cut disks from a 1 metre wide sheet of aluminium, delivered on rolls of 100 metres. How should the machine best be configured?
2. (Original post by Spiral1977)
(A) At present a disk-pressing machine is set to cut out 16 disks, each of diameter 0.25m, from a 1 square metre aluminium sheet. There is also a further need to cut disks, each of diameter 0.1m, from the same sheets. The firm needs twice the number of small disks as they do large disks. What is the best arrangement of cutting heads to minimise wastage?

(B) As an extension, and more generally, the manager wants to invest in a continuous strip processing machine, that will cut disks from a 1 metre wide sheet of aluminium, delivered on rolls of 100 metres. How should the machine best be configured?
i do not personally know a formal method
I would draw the square metre sheet and "play" with the diagram to start with

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Updated: November 6, 2015
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