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On the left I have the following data from a client, and need to turn into the table on the right. The date columns are dynamic - they vary weekly and the resulting pivot table should react when date columns get added/removed.

If a customer/product has more than one date column with value, the new table should have more than one row to accommodate only one value per row.

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Actually, it appears that you want to "de-pivot" your data. Here's a situation very similar to yours, with a detailed step-by-step solution:
de-pivoting

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Yes, this is what pivot tables are for, and see here for a tutorial on how to use them. They wrote instructions better than I can.

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