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How to fit rectangles in a given area?

Having a known increment for the Yi means that knowing Y1 you can find all other Yi, and subsequently all Xi (from the circle equation (Sum Xi)^2 + Yi^2/4 = R^2). And from these, the covered area.

This establishes a relation between Y1 and the objective function. First plot it so see how the maxima(s) look like (piecewise smooth but discontinuous). Then... call the team again.

For ease of work in Excel, you can proceed with a fixed number of rectangles and set a zero Xi for those that get out of the circle.





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