The correct answer is: A. Only one input is fixed and all other inputs are kept variable.
The law of variable proportions states that in the short run, when one input is fixed and all other inputs are increased, there will be a point at which the marginal product of the variable input will decline.
Option B is incorrect because all factors cannot be kept constant in the short run. At least one factor must be fixed in order to measure the marginal product of the variable input.
Option C is incorrect because the law of variable proportions does not state that all inputs must vary in the same proportion. In fact, the law states that the marginal product of the variable input will decline even if all other inputs are increased in the same proportion.
Option D is incorrect because the law of variable proportions is a valid economic principle. It is a well-established theory that has been supported by empirical evidence.