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Mixed Batch Labor Cost Problem Help

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This is a Real World Factory. I have a production line that provides 12 different products in various sizes on demand. I know the products, their sizes and the total labor for each batch. The problem is to calculate the labor cost of each product. They are produced in mixed batches where different product types are produced at the same time.  
My assumption is that each product has an initial labor cost plus additional incremental labor costs for each additional size larger than standard, which may or may not be a straight line.

 Is it possible to determine cost based on analyzing the composition of these batches without using brute force programming?

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