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A large drop in material costs as a result of purchasing material from a foreign source would reduce M in the model, which would decrease the cost of the product. This would be consistent with the model and would not serve to invalidate its results.
The model is supposed to estimate the cost of the product. Therefore, the "a" in the formula does not represent actual labor hours used to produce the product. The "a" in the formula represents the standard number of hours allowed for production of the product. If labor productivity were to decrease, the actual number of labor hours required to produce the product would increase; and if labor productivity were to increase, the actual number of labor hours required would decrease. However, since the "a" represents the standard number of hours required to produce the actual output, the "a" would not change because of a change in labor productivity. The estimated cost resulting from the model would be significantly different from the actual cost to produce the product. This would have the greatest impact on invalidating the results of the model.
Renegotiation of the union contract calling for much higher wage rates would increase the L in the model, which would increase the cost of the product. This would be consistent with the model and would not serve to invalidate its results.
A significant reduction in factory overheads would reduce FC in the model, which would decrease the cost of the product. This would be consistent with the model and would not serve to invalidate its results.